Middle School Science Quiz: Model Potential Energy
20 questions · exam conditions
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Model Potential EnergyQuestion 1 of 20

A 2 kg toolbox is lifted from the floor (reference level) up to a shelf 3 m high. Use g≈10 m/s2g \approx 10\,\text{m/s}^2. How much gravitational potential energy does the toolbox gain?

6 J
15 J
60 J
90 J
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Middle School Science Quiz

Middle School Science Quiz: Model Potential Energy

Practice Model Potential Energy in Middle School Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Model Potential Energy, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

A 2 kg toolbox is lifted from the floor (reference level) up to a shelf 3 m high. Use g≈10 m/s2g \approx 10\,\text{m/s}^2. How much gravitational potential energy does the toolbox gain?

  1. 6 J
  2. 15 J
  3. 60 J (correct answer)
  4. 90 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy gained is calculated using ΔPE = mgh: mass m = 2 kg, gravitational field strength g = 10 m/s², height change Δh = 3 m from floor, so ΔPE = (2 kg)(10 m/s²)(3 m) = 60 J. This means the toolbox gains 60 Joules of gravitational potential energy—if it were to fall from 3 m to the floor, this 60 J of PE would convert to kinetic energy. Choice C is correct because it correctly calculates PE = mgh = (2)(10)(3) = 60 J with proper substitution. Choice B is wrong because it makes a calculation error: perhaps using wrong g or arithmetic mistake like (2)(10)(1.5) or (3)(10)(0.5), but the full height is 3 m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 2

A 3 kg backpack is on a shelf 2 m above the floor. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, what is its gravitational potential energy relative to the floor?

  1. 15 J
  2. 6 J
  3. 60 J (correct answer)
  4. 120 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 3 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 2 m above the floor (reference level), so PE = (3 kg)(10 m/s²)(2 m) = 60 J. Choice C is correct because it accurately calculates PE = mgh = (3)(10)(2) = 60 J with proper substitution. Choice A is wrong because it makes a calculation error: uses wrong mass or height, like (1.5)(10)(1) = 15 J or similar mistake. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 3

A 5 kg object has gravitational potential energy of 150 J relative to the ground. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, how high above the ground is the object?

  1. 15 m
  2. 3 m (correct answer)
  3. 30 m
  4. 0.3 m
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). To find height from PE, rearrange h = PE / (mg): PE = 150 J, m = 5 kg, g = 10 m/s², so h = 150 / (5 × 10) = 150 / 50 = 3 m above the ground. Choice B is correct because it properly applies the rearranged formula to determine h = PE / (mg) = 150 / 50 = 3 m. Choice A is wrong because it makes a calculation error: perhaps h = 150 / (5 × 2) = 15 m or using wrong g. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 4

The same 1 kg1\text{ kg} book is first on the floor (0 m0\text{ m}) and then moved to a low shelf (1 m1\text{ m}) above the floor. Using g≈10 m/s2g \approx 10\text{ m/s}^2, how much does the book's gravitational potential energy increase?

  1. 1 J1\text{ J}
  2. 0 J0\text{ J}
  3. 10 J10\text{ J} (correct answer)
  4. 100 J100\text{ J}
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). To find the increase in gravitational potential energy, calculate PE at each position and find the difference: initially on floor (h = 0 m), PE₁ = (1 kg)(10 m/s²)(0 m) = 0 J; on low shelf (h = 1 m), PE₂ = (1 kg)(10 m/s²)(1 m) = 10 J; therefore, increase in PE = PE₂ - PE₁ = 10 J - 0 J = 10 J. This 10 J increase represents the work you did lifting the book from floor to shelf—you applied an upward force equal to the book's weight (mg = 10 N) through a distance of 1 m, doing work = force × distance = 10 N × 1 m = 10 J, which is now stored as gravitational potential energy. Choice C is correct because it accurately calculates the change in PE as 10 J when moving from 0 m to 1 m height. Choice A (1 J) appears to have omitted g, calculating just m×Δh = 1×1 = 1 J; Choice B (0 J) incorrectly suggests no change in PE despite changing height; Choice D (100 J) makes an arithmetic error, possibly calculating 1×10×10 instead of 1×10×1. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 1 m shelf increases its PE by (1)(10)(1) = 10 J—you did 10 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 10 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 5

A roller coaster cart has a mass of 500 kg500\text{ kg}. At the top of a hill it is 20 m20\text{ m} above the ground (reference level). Using g≈10 m/s2g \approx 10\text{ m/s}^2, what is its gravitational potential energy at the top?

  1. 10,000 J10{,}000\text{ J}
  2. 50,000 J50{,}000\text{ J}
  3. 100,000 J100{,}000\text{ J} (correct answer)
  4. 1,000 J1{,}000\text{ J}
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 500 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 20 m above the ground (reference level), so PE = (500 kg)(10 m/s²)(20 m) = 100,000 J. This means the roller coaster cart has 100,000 Joules of gravitational potential energy at the top of the hill—if it were to roll down from 20 m height to ground level, this 100,000 J of PE would convert to kinetic energy (in ideal case with no friction, KE at ground would be 100,000 J, giving the cart significant speed). Choice C is correct because it correctly calculates PE = mgh = (500)(10)(20) = 100,000 J with proper substitution. Choice A (10,000 J) appears to have made an arithmetic error, possibly calculating 500×20 = 10,000 without including g; Choice B (50,000 J) might have used wrong height (10 m instead of 20 m) giving 500×10×10 = 50,000; Choice D (1,000 J) severely underestimates, perhaps dividing instead of multiplying or using wrong values. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: a 500 kg roller coaster cart at 20 m height has PE = 100,000 J—this enormous energy was provided by the lift mechanism pulling the cart up the first hill, and as the cart descends, this PE converts to KE making the ride thrilling; water behind a dam at similar heights stores millions of joules as gravitational PE, which converts to flowing water's KE to spin turbines for hydroelectric power.

Question 6

A 2 kg backpack is lifted from the floor (reference level, h=0h=0 m) to a hook that is 3 m above the floor. Using g≈10 m/s2g \approx 10\ \text{m/s}^2, how much gravitational potential energy does the backpack gain?

  1. 5 J
  2. 30 J
  3. 60 J (correct answer)
  4. 600 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy gained is calculated using ΔPE = mgΔh: mass m = 2 kg, g = 10 m/s², change in height Δh = 3 m (from 0 m to 3 m), so ΔPE = (2)(10)(3) = 60 J. Choice C is correct because it accurately calculates the gain in PE = mgΔh = (2)(10)(3) = 60 J with proper substitution. Choice A is wrong because it makes a calculation error: arithmetic mistake like (2)(10)(0.25) or using wrong height, resulting in 5 J, when actually it's 60 J for 3 m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 7

A 1 kg book is on a shelf 2 m above the ground. Using g≈10 m/s2g \approx 10\ \text{m/s}^2, its gravitational potential energy is calculated using h=2h=2 m. If a student instead chooses the top of a 1 m-high table as the reference level (so the shelf is 1 m above this new reference), what happens to the calculated gravitational potential energy value for the book?

  1. It becomes 0 J because the book is on a shelf.
  2. It becomes 10 J because the height above the new reference is 1 m. (correct answer)
  3. It stays 20 J because reference level never matters.
  4. It becomes 30 J because the heights add.
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). With the new reference at the 1 m table, the shelf is now at h = 1 m above the reference, so PE = (1 kg)(10 m/s²)(1 m) = 10 J, compared to original PE = (1)(10)(2) = 20 J using ground as reference—the calculated value changes with reference level, but differences in PE (like changes) remain the same regardless of reference. Choice B is correct because it appropriately applies the formula to the new reference, calculating PE = mgh with h=1 m giving 10 J. Choice A is wrong because it confuses reference point incorrectly: claims PE becomes 0 J just because it's on a shelf, but PE is relative to the chosen reference and is not zero unless h=0. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 8

A 3 kg object has gravitational potential energy of 150 J relative to the ground. Using g≈10 m/s2g \approx 10\,\text{m/s}^2, how high above the ground is the object?

  1. 0.5 m
  2. 3 m
  3. 5 m (correct answer)
  4. 15 m
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). To find height, rearrange PE = mgh to h = PE / (mg): with PE = 150 J, m = 3 kg, g = 10 m/s², h = 150 / (3×10) = 150 / 30 = 5 m. This means the object is 5 m above the ground, storing 150 J of PE that could convert to KE if it falls. Choice C is correct because it correctly calculates h = PE / (mg) = 150 / (3×10) = 5 m. Choice D is wrong because it makes a calculation error: perhaps omitting m and calculating 150 / 10 = 15 m, but mass must be included since PE ∝ m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 9

Three objects sit on a table that is 1.5 m above the ground (ground is the reference level). Their masses are 1 kg, 2 kg, and 5 kg. Using g≈10 m/s2g \approx 10\,\text{m/s}^2, which object has the greatest gravitational potential energy?

  1. The 1 kg object
  2. The 2 kg object
  3. The 5 kg object (correct answer)
  4. All three have the same gravitational potential energy because they are at the same height
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). At the same height h = 1.5 m, comparing different masses: 1 kg object has PE = (1)(10)(1.5) = 15 J, 2 kg object has PE = (2)(10)(1.5) = 30 J, and 5 kg object has PE = (5)(10)(1.5) = 75 J—the 5 kg has the greatest, showing gravitational potential energy is directly proportional to mass at constant height: PE ∝ m. The heavier object has more PE at the same height because it required more work to lift it there (lifting 5 kg through 1.5 m takes more work than lifting 1 kg through same 1.5 m), and it stores that work as gravitational potential energy. Choice C is correct because it properly identifies the proportional relationship: greater mass → greater PE at same height. Choice D is wrong because it misunderstands proportionality: claims all have same PE since same height, but actually PE ∝ m, so different masses have different PE even at same h. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 10

Two identical 2 kg backpacks are compared using g≈10 m/s2g \approx 10\,\text{m/s}^2 and the ground as h=0h=0 m. Backpack A is 1 m above the ground, and Backpack B is 3 m above the ground. How does the gravitational potential energy of Backpack B compare to Backpack A?

  1. Backpack B has one-third the potential energy of Backpack A.
  2. Backpack B has the same potential energy as Backpack A.
  3. Backpack B has 2 times the potential energy of Backpack A.
  4. Backpack B has 3 times the potential energy of Backpack A. (correct answer)
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). Comparing identical 2 kg backpacks: Backpack A at h = 1 m has PE = (2)(10)(1) = 20 J, Backpack B at h = 3 m has PE = (2)(10)(3) = 60 J, so B has 60 / 20 = 3 times the PE of A, since heights are in ratio 3:1 and PE ∝ h. Choice D is correct because it accurately compares PE values showing triple height means triple PE. Choice A is wrong because it claims inverse relationship: one-third, but actually PE ∝ h is direct (triple h → triple PE). Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 11

A roller coaster cart has a mass of 500 kg. Take g≈10 m/s2g \approx 10\,\text{m/s}^2 and define the ground as h=0h=0 m. Which position gives the cart the greatest gravitational potential energy: at 0 m, at 10 m, or at 20 m above the ground?

  1. At 0 m
  2. At 10 m
  3. At 20 m (correct answer)
  4. All positions have the same gravitational potential energy
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). Comparing the same 500 kg cart at different heights: at h = 0 m, PE = (500)(10)(0) = 0 J, at h = 10 m, PE = (500)(10)(10) = 5000 J, and at h = 20 m, PE = (500)(10)(20) = 10000 J—the greatest PE is at 20 m, demonstrating that gravitational potential energy is directly proportional to height: PE ∝ h. Choice C is correct because it accurately compares PE values showing the highest height has the most PE. Choice A is wrong because it reverses the comparison: claims 0 m has the greatest PE, when PE = mgh shows higher h gives more PE. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction). Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 12

A roller coaster cart has a mass of 500 kg. Take g≈10 m/s2g\approx 10\,\text{m/s}^2 and define the ground as h=0h=0 m. What is the cart's gravitational potential energy at the top of a hill that is 20 m above the ground?

  1. 10,000 J
  2. 1,000 J
  3. 100,000 J (correct answer)
  4. 50,000 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 500 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 20 m above the ground (reference level), so PE = (500 kg)(10 m/s²)(20 m) = 100,000 J. Choice C is correct because it accurately calculates PE = mgh = (500)(10)(20) = 100,000 J with proper substitution. Choice A is wrong because it makes an arithmetic mistake: calculates (500)(10)(2) = 10,000 J, perhaps misreading height as 2 m instead of 20 m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 13

A 1 kg book is placed on different shelves. The floor is the reference level where h=0h=0 m and PE=0PE=0 J. Use g≈10 m/s2g\approx 10\,\text{m/s}^2. What is the book's gravitational potential energy when it is on the high shelf at h=2h=2 m?

  1. 2 J
  2. 20 J (correct answer)
  3. 10 J
  4. 200 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 1 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 2 m above the floor (reference level), so PE = (1 kg)(10 m/s²)(2 m) = 20 J. Choice B is correct because it accurately calculates PE = mgh = (1)(10)(2) = 20 J with proper substitution. Choice A is wrong because it makes a calculation error: omits g and just does mh = (1)(2) = 2 J, forgetting the gravitational field strength factor. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 14

Three objects sit on a table that is 1.5 m above the floor (floor is the reference level). The objects have masses 1 kg, 2 kg, and 5 kg. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, which object has the greatest gravitational potential energy relative to the floor?

  1. The 1 kg object
  2. The 2 kg object
  3. All three have the same gravitational potential energy
  4. The 5 kg object (correct answer)
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). At the same height h = 1.5 m, comparing different masses: 1 kg object has PE = (1)(10)(1.5) = 15 J, 2 kg object has PE = (2)(10)(1.5) = 30 J, and 5 kg object has PE = (5)(10)(1.5) = 75 J—the 5 kg object has the greatest PE, demonstrating that gravitational potential energy is directly proportional to mass at constant height: PE ∝ m. Choice D is correct because it properly identifies that the 5 kg object has the most PE since PE ∝ m and 5 kg is the largest mass at the same height. Choice C is wrong because it claims all have the same PE, misunderstanding that PE depends on mass (PE ∝ m), not just height—different masses at same h have different PE. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 15

A 2 kg object is lifted from h=1h=1 m to h=4h=4 m above the ground (ground is the reference level). Use g≈10 m/s2g\approx 10\,\text{m/s}^2. How much does its gravitational potential energy increase?

  1. 60 J (correct answer)
  2. 80 J
  3. 30 J
  4. 10 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The increase in gravitational potential energy is calculated as ΔPE = mg Δh: mass m = 2 kg, g = 10 m/s², Δh = 4 m - 1 m = 3 m, so ΔPE = (2)(10)(3) = 60 J (alternatively, PE at 1 m = 20 J, at 4 m = 80 J, increase = 60 J). Choice A is correct because it accurately calculates the increase in PE as mg Δh = (2)(10)(3) = 60 J. Choice B is wrong because it calculates PE at 4 m = 80 J but forgets to subtract the initial PE, giving the final PE instead of the increase. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 16

A 1 kg book is on a shelf that is 2 m above the floor. If you choose a new reference level at 1 m above the floor, what is the book's gravitational potential energy relative to this new reference? Use g≈10 m/s2g\approx 10\,\text{m/s}^2.

  1. 20 J
  2. 0 J
  3. 10 J (correct answer)
  4. 5 J
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). With the new reference at 1 m above the floor, the book's height relative to this reference is 2 m - 1 m = 1 m, so PE = (1 kg)(10 m/s²)(1 m) = 10 J (note that changing reference shifts all PE values by a constant, but differences remain the same). Choice C is correct because it appropriately applies the formula to the new reference level, calculating PE = mgh with h=1 m relative to the new zero. Choice B is wrong because it claims 0 J, perhaps confusing the new reference with the book's position, but the book is 1 m above the new reference so PE=10 J ≠0. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 17

A 4 kg object is raised from 2 m to 6 m above the ground. If g≈10 m/s2g\approx 10\,\text{m/s}^2, how does its gravitational potential energy at 6 m compare to its gravitational potential energy at 2 m?

  1. It is 3 times as large (correct answer)
  2. It is 4 times as large
  3. It is 2 times as large
  4. It is 13\tfrac{1}{3} as large
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). Comparing the same 4 kg object at different heights: at h = 2 m, PE = (4)(10)(2) = 80 J, and at h = 6 m, PE = (4)(10)(6) = 240 J—the PE is 240/80 = 3 times as large when height is 6/2 = 3 times as large, demonstrating that gravitational potential energy is directly proportional to height: PE ∝ h. Choice A is correct because it properly identifies the proportional relationship: triple height (2 → 6 m) → triple PE. Choice B is wrong because it applies wrong relationship: claims 4 times, perhaps confusing with something else, but actually PE ∝ h is linear (triple h → triple PE, not quadruple). Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Water behind dam at height h has gravitational PE = mgh (enormous for millions of kg of water at tens of meters height), which converts to KE as water flows down through turbines (hydroelectric power: stored PE → flowing KE → rotational KE of turbine → electrical energy), showing how gravitational PE is useful stored energy we can harness.

Question 18

A pendulum bob has mass 2 kg. The lowest point of the swing is chosen as the reference level (h=0h=0 m). At each endpoint of the swing, the bob is 0.5 m above the lowest point. Using g≈10 m/s2g\approx 10\,\text{m/s}^2, what is the bob's gravitational potential energy at an endpoint (relative to the lowest point)?

  1. 0 J
  2. 5 J
  3. 100 J
  4. 10 J (correct answer)
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The gravitational potential energy is calculated using PE = mgh: mass m = 2 kg, gravitational field strength g = 10 m/s² (on Earth), height h = 0.5 m above the lowest point (reference level), so PE = (2 kg)(10 m/s²)(0.5 m) = 10 J. Choice D is correct because it accurately calculates PE = mgh = (2)(10)(0.5) = 10 J with proper substitution. Choice A is wrong because it claims 0 J, perhaps confusing the endpoint with the lowest point where PE=0, but at endpoint h=0.5 m >0 so PE>0. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 19

A 3 kg object has gravitational potential energy of 90 J relative to the ground (ground is the reference level). Using g≈10 m/s2g \approx 10\ \text{m/s}^2, what is the object's height above the ground?

  1. 0.3 m
  2. 3 m (correct answer)
  3. 30 m
  4. 300 m
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). The height is calculated by rearranging PE = mgh to h = PE / (mg): PE = 90 J, m = 3 kg, g = 10 m/s², so h = 90 / (3 × 10) = 90 / 30 = 3 m. Choice B is correct because it accurately calculates h = PE / (mg) = 90 / (3 × 10) = 3 m with proper substitution. Choice A is wrong because it makes a calculation error: arithmetic mistake like 90 / (3 × 100) or using g=100, resulting in 0.3 m, when actually g=10 gives 3 m. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).

Question 20

Three objects sit on the same table that is 1.5 m above the floor (floor is the reference level). Object A has mass 1 kg, Object B has mass 2 kg, and Object C has mass 5 kg. Using g≈10 m/s2g \approx 10\ \text{m/s}^2, which object has the greatest gravitational potential energy due to its position?

  1. Object A (1 kg)
  2. Object B (2 kg)
  3. Object C (5 kg) (correct answer)
  4. All three have the same gravitational potential energy because the height is the same
Explanation: This question tests understanding of gravitational potential energy calculated using PE = mgh, where energy depends on mass, height, and gravitational field strength. Gravitational potential energy (PE = mgh) is the energy an object has due to its position in a gravitational field—specifically, its height above some chosen reference level: an object at height h has the potential to fall through that height, converting potential energy to kinetic energy, and the amount of PE represents how much work was done to lift the object to that height (or how much work it could do falling back down). The formula shows three factors: m is the object's mass in kilograms (more mass → more PE), g is Earth's gravitational field strength ≈ 10 m/s² or 10 N/kg (on Earth's surface, essentially constant), and h is height in meters above the chosen reference level where PE = 0 (ground, floor, table—you choose the reference). At the same height h = 1.5 m, comparing different masses: 1 kg object has PE = (1)(10)(1.5) = 15 J, 2 kg object has PE = (2)(10)(1.5) = 30 J, and 5 kg object has PE = (5)(10)(1.5) = 75 J—gravitational potential energy is directly proportional to mass at constant height: PE ∝ m. Choice C is correct because it properly identifies the proportional relationship: the 5 kg object has the greatest PE since PE ∝ m and 5 kg is the largest mass. Choice D is wrong because it misunderstands proportionality: claims all have same PE since height is same, but actually PE also depends on mass (PE ∝ m), so heavier objects have more PE at the same height. Working with gravitational potential energy: (1) choose reference level where PE = 0 (usually ground or lowest point in scenario), (2) measure all heights from this reference (height above = positive h, below would be negative h), (3) calculate PE = mgh for each position using mass in kg, g = 10 m/s², height in m, (4) compare: higher positions have more PE (proportional to h), heavier objects have more PE at same height (proportional to m), and (5) understand meaning: PE is energy stored by position, represents work done lifting object, can convert to KE if object falls. Practical examples: lifting 1 kg book from floor to 2 m shelf increases its PE by (1)(10)(2) = 20 J—you did 20 J of work lifting it, and that energy is now stored as PE; if book falls back to floor, that 20 J converts to KE as it falls (speeds up gaining kinetic energy while losing potential energy, total mechanical energy conserved if no friction).