Gravity Depends on Mass - Middle School Physical Science

A 1 kg object is weighed on three different planets. The measured gravitational force (weight) is shown below. Planet | Weight of 1 kg object (N) Mars | 3.7 Earth | 10 Jupiter | 25 Which statement best matches the pattern in the data?
Answer: More massive planets tend to have stronger surface gravity, so a 1 kg object weighs more there. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. Comparing planets with different masses shows that more massive planets have stronger surface gravity: Mars (lower mass than Earth) has weaker gravity (g = 3.7 m/s², so 1 kg object weighs only 3.7 N), Earth (medium mass) has moderate gravity (g = 10 m/s², so 1 kg weighs 10 N), and Jupiter (much more massive than Earth) has very strong gravity (g = 25 m/s², so 1 kg weighs 25 N)—the planet's mass determines its gravitational field strength, which determines how much objects weigh on that planet. Choice A is correct because it properly explains that massive planets have stronger gravity because their large mass creates stronger gravitational fields. Choice C is wrong because it claims less massive planets have stronger gravity, but the data show Mars (less massive) has weaker gravity than Earth or Jupiter. Understanding this helps explain why astronauts on Mars could jump higher due to weaker gravity pulling them down.
A $1\ \text{kg}$ object weighs $10\ \text{N}$ on Earth and $25\ \text{N}$ on Jupiter. Which statement best explains why the same object has a larger weight on Jupiter?
Answer: Jupiter's stronger gravity exerts a larger gravitational force on the same mass. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. Comparing planets with different masses shows that more massive planets have stronger surface gravity: the 1 kg object weighs 10 N on Earth (where g = 10 m/s²) but 25 N on Jupiter (where g = 25 m/s²)—the planet's greater mass creates a stronger gravitational field, which exerts a larger force on any object at its surface. Choice B is correct because it properly explains that Jupiter's stronger gravity (due to its much larger mass) exerts a larger gravitational force on the same 1 kg mass—the object's mass remains 1 kg everywhere, but the gravitational field strength g varies with the planet's mass. Choice A (mass increases on Jupiter) incorrectly claims the object's mass changes between planets when only weight changes; Choice C (gravity doesn't depend on planet) contradicts the data showing different weights on different planets; Choice D (Jupiter has weaker gravity) reverses the relationship, claiming Jupiter pulls less when it actually pulls more (25 N > 10 N). Understanding gravitational force's dependence on mass: (1) same object has different weights on different planets because g varies with planet mass: weight = mass × g, so 1 kg weighs 1 × 10 = 10 N on Earth but 1 × 25 = 25 N on Jupiter, (2) the planet's mass determines its gravitational field strength at the surface. Practical implications: future Jupiter missions must account for the crushing 2.5× Earth gravity—equipment designed for Earth would need reinforcement, and human visitors would struggle to stand or move normally under their increased weight.
On Earth ( $g \approx 10\ \text{N/kg}$ ), an apple has mass $0.1\ \text{kg}$ , a book has mass $1\ \text{kg}$ , and a person has mass $70\ \text{kg}$ . Their approximate weights are listed below. Object | Mass (kg) | Weight (N) Apple | 0.1 | 1 Book | 1 | 10 Person | 70 | 700 What does the table show about the relationship between mass and weight on Earth?
Answer: Weight is directly proportional to mass: larger mass means larger weight. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 70 kg person weighs 700 N on Earth while a 0.1 kg apple weighs 1 N (700 times mass, 700 times weight). The data clearly demonstrate proportionality: apple 0.1 kg → 1 N, book 1 kg → 10 N, person 70 kg → 700 N, showing weight = 10 × mass consistently. Choice C is correct because it accurately identifies the proportional relationship: larger mass means larger weight. Choice A is wrong because it claims inverse relationship, but data show as mass increases, weight increases (not decreases). This understanding clarifies why mass and weight are different: mass is constant, but weight varies with g.
On Earth, the gravitational force (weight) on an object is about $10\ \text{N}$ for every $1\ \text{kg}$ of mass. A student measures these weights on Earth: Mass (kg) → Weight (N) 0.5 → 5 1.0 → 10 2.0 → 20 Based on this pattern, what would be the weight of a $3\ \text{kg}$ object on Earth?
Answer: 30 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The data clearly demonstrate proportionality: an object with mass 0.5 kg has weight 5 N on Earth, 1 kg object has weight 10 N (doubled), 2 kg object has weight 20 N (doubled again)—each time mass doubles, weight doubles, showing the linear proportional relationship. Choice B is correct because it accurately identifies that a 3 kg object would weigh 30 N (3 × 10 = 30), following the established pattern of 10 N per kg. Choice A (13 N) makes no mathematical sense given the clear 10 N/kg pattern; Choice C (6 N) would mean weight decreases as mass increases from 2 kg to 3 kg, contradicting the data; Choice D (20 N) incorrectly suggests the same weight for 3 kg as for 2 kg, ignoring the proportional relationship. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight). Practical implications: this proportional relationship explains why shipping costs often depend on weight—heavier packages require more fuel to transport because they experience stronger gravitational force that must be overcome.
On Earth, a 2 kg object has weight 20 N. If you keep the same planet and double the object's mass to 4 kg, what happens to the gravitational force (weight)?
Answer: It becomes 40 N because weight is proportional to mass on the same planet. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 4 kg object weighs 40 N on Earth while a 2 kg weighs 20 N (twice the mass, twice the weight). With g constant on Earth, doubling mass from 2 kg to 4 kg doubles weight from 20 N to 40 N. Choice B is correct because it correctly predicts that doubling mass doubles gravitational force. Choice D is wrong because it claims doubling mass quadruples weight, violating proportionality (should double, not quadruple). Understanding this helps in engineering, like calculating forces in elevators carrying varying loads.
On Earth, $g \approx 10\ \text{N/kg}$ . A book has a mass of 1.5 kg. What is the book's weight (gravitational force) on Earth?
Answer: 15 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This pattern holds because weight is calculated as W = mg (mass × gravitational field strength), and with g = 10 m/s² constant on Earth's surface, weight must be proportional to mass: W = 10m means a 1.5 kg book has weight = 1.5 kg × 10 m/s² = 15 N. Choice C is correct because it accurately calculates the book's weight using the proportional relationship: 1.5 kg × 10 m/s² = 15 N. Choice A (1.5 N) makes calculation error by not multiplying mass by g; Choice B (10 N) incorrectly uses 1 kg instead of 1.5 kg given in problem; Choice D (150 N) makes decimal error suggesting 15 kg was used instead of 1.5 kg. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).
A person has a mass of 70 kg. Using $g \approx 10\ \text{N/kg}$ on Earth and $g \approx 1.6\ \text{N/kg}$ on the Moon, which pair of weights is closest to correct?
Answer: Earth: 700 N; Moon: 112 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The data clearly demonstrate proportionality: a person with mass 70 kg has weight W = mg = 70 kg × 10 N/kg = 700 N on Earth, and on the Moon where g = 1.6 N/kg, the same person has weight W = 70 kg × 1.6 N/kg = 112 N—mass stays constant at 70 kg but weight changes with gravitational field strength, being about 1/6 as much on the Moon as on Earth. Choice B is correct because it accurately calculates both weights: Earth weight = 70 kg × 10 N/kg = 700 N, Moon weight = 70 kg × 1.6 N/kg = 112 N. Choice A reverses the values, putting the smaller weight on Earth and larger on Moon when Moon's weaker gravity must produce smaller weight; Choice C incorrectly uses 70 N as Earth weight (should be 700 N) and 1.6 N as Moon weight (confusing g value with actual weight); Choice D claims weight is same on both, when different g values must produce different weights for same mass. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), (3) mass remains constant—the 70 kg person has 70 kg of matter whether on Earth or Moon, but experiences different gravitational forces. Practical implications: Apollo astronauts could jump much higher on the Moon despite heavy spacesuits because their weight was reduced to 1/6 Earth value—understanding this mass-weight distinction was crucial for designing lunar equipment and planning moonwalk activities where objects felt lighter but still had full inertia.
A student says: "If two objects are at the same distance apart, the gravitational force between them depends on the masses of both objects." Which piece of evidence best supports this idea? Trial | Mass of object A (kg) | Mass of object B (kg) | Force (N) 1 | 2 | 3 | 6 2 | 4 | 3 | 12 3 | 2 | 6 | 12
Answer: Changing either mass changes the force, and doubling one mass doubles the force. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: comparing trials 1 and 2, when Object A's mass doubles from 2 kg to 4 kg (keeping Object B at 3 kg), force doubles from 6 N to 12 N; comparing trials 1 and 3, when Object B's mass doubles from 3 kg to 6 kg (keeping Object A at 2 kg), force also doubles from 6 N to 12 N—this demonstrates that gravitational force depends on both masses, with each contributing proportionally to the total force. Choice A is correct because it accurately identifies that changing either mass changes the force, and doubling one mass doubles the force. Choice B incorrectly claims only object A matters, but trial 3 shows changing B's mass (while keeping A constant) also changes force; Choice C incorrectly claims only object B matters, but trial 2 shows changing A's mass (while keeping B constant) also changes force; Choice D claims force stays constant, when the data clearly show force varying from 6 N to 12 N across trials. Understanding gravitational force's dependence on mass: (1) gravitational force between two objects depends on both their masses, following F = Gm₁m₂/r² where both masses multiply together, (2) doubling either mass doubles the force because of the multiplication: if m₁ doubles, then Gm₁m₂/r² doubles; if m₂ doubles, then Gm₁m₂/r² also doubles, (3) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law). Practical implications: this mutual dependence explains tidal forces—the Moon's gravity pulls on Earth's oceans, but Earth's gravity also pulls on the Moon, creating a two-body system where both masses matter for calculating orbital dynamics and tidal patterns.
On Earth, the gravitational force (weight) on an object is about $10\ \text{N}$ for every $1\ \text{kg}$ of mass. A student measures these weights on Earth: Mass (kg) → Weight (N) - 1 kg → 10 N - 2 kg → 20 N - 4 kg → 40 N What does this data show about how gravitational force (weight) depends on mass on Earth?
Answer: Weight is directly proportional to mass (doubling the mass doubles the weight). This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The data clearly demonstrate proportionality: an object with mass 1 kg has weight 10 N on Earth, 2 kg object has weight 20 N (doubled), 4 kg object has weight 40 N (doubled again)—each time mass doubles, weight doubles, showing the linear proportional relationship. Choice B is correct because it accurately identifies the proportional relationship: more mass → more gravitational force, specifically stating that doubling the mass doubles the weight, which matches the data exactly (1 kg→10 N, 2 kg→20 N, 4 kg→40 N). Choice A reverses the relationship, claiming more mass produces less gravitational force when the data clearly show weight increases with mass; Choice C claims mass doesn't affect gravitational force, when the entire dataset demonstrates that mass is the primary factor determining weight; Choice D suggests weight increases faster than mass (doubling mass triples weight), but the data show exact doubling: 2 kg gives 20 N (not 30 N), 4 kg gives 40 N (not 60 N). Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight). This pattern holds because weight is calculated as W = mg (mass × gravitational field strength), and with g = 10 m/s² constant on Earth's surface, weight must be proportional to mass: W = 10m means doubling m doubles W.
A simple simulation keeps distance the same and changes only one mass. When Mass A is kept at 2 kg, the gravitational force changes like this: Mass B (kg) → Force (units) - 1 → 4 - 2 → 8 - 3 → 12 Based on the pattern, what would the force be when Mass B is $5\ \text{kg}$ ?
Answer: 20 This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: when Mass B increases from 1 kg to 2 kg (doubles), force increases from 4 to 8 units (doubles); when Mass B goes from 2 kg to 3 kg, force goes from 8 to 12 units—this demonstrates that gravitational force is proportional to each mass, with the pattern showing force = 4 × Mass B (when Mass A = 2 kg). Choice C is correct because it correctly predicts that when Mass B = 5 kg, the force will be 4 × 5 = 20 units, following the established pattern where force is proportional to Mass B (each kg of Mass B contributes 4 units of force when Mass A = 2 kg). Choice A (10 units) would mean only 2 units per kg of Mass B, contradicting the pattern; Choice B (16 units) doesn't follow the proportional relationship; Choice D (25 units) would mean 5 units per kg, also violating the observed pattern of 4 units per kg of Mass B. Understanding gravitational force's dependence on mass: (1) gravitational force depends on both masses multiplicatively—doubling either mass doubles the force, as shown in the simulation, (2) the relationship F ∝ m₁m₂ means force is proportional to the product of the two masses, which explains why the force increases linearly with Mass B when Mass A is held constant. This principle explains why massive objects like planets exert strong gravitational forces (they have enormous mass), and why the gravitational force between everyday objects is too small to notice (both masses are relatively small, making their product tiny compared to forces involving Earth's mass).
On Earth, a 3 kg object has a weight of about 30 N (using $g \approx 10\,\text{N/kg}$ ). If the mass is doubled to 6 kg, what will the object's weight be on Earth?
Answer: 60 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. This relationship explains why heavier objects (more mass) weigh more (experience stronger gravitational force): a 2 kg book weighs 20 N on Earth while a 1 kg book weighs 10 N (twice the mass, twice the weight). The data clearly demonstrate proportionality: an object with mass 3 kg has weight 30 N on Earth, and when doubled to 6 kg, the weight should double to 60 N, following the pattern where each time mass doubles, weight doubles, showing the linear proportional relationship. Choice C is correct because it accurately identifies the proportional relationship: more mass → more gravitational force / correctly predicts that doubling mass doubles weight. Choice B is wrong because it suggests weight stays at 30 N or doesn't fully double, when the pattern shows exact doubling: doubling from 3 kg to 6 kg should go from 30 N to 60 N. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).
Two objects are the same distance apart in a simulation. In Trial 1, the masses are 2 kg and 5 kg and the gravitational force is 10 units. In Trial 2, only the 2 kg mass is changed to 4 kg (distance and the 5 kg mass stay the same). What gravitational force should the simulation report in Trial 2?
Answer: 20 units This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force doubles; this relationship is shown by Newton's law of gravitation where F ∝ m₁m₂ (force is proportional to the product of both masses), meaning if either mass doubles, the force doubles. The simulation results show that increasing either mass increases the gravitational force between two objects: in Trial 1 with masses 2 kg and 5 kg, the force is 10 units; in Trial 2, doubling the first mass from 2 kg to 4 kg (keeping the 5 kg mass and distance constant) should double the force from 10 to 20 units—this demonstrates that gravitational force is proportional to each mass individually. Choice C is correct because it accurately predicts that doubling one mass from 2 kg to 4 kg doubles the gravitational force from 10 units to 20 units, maintaining the proportional relationship F ∝ m₁. Choice A (5 units) would mean halving the force when mass doubles; Choice B (10 units) incorrectly suggests force doesn't change when mass doubles; Choice D (40 units) would mean quadrupling the force when mass only doubles, violating proportionality. Understanding gravitational force's dependence on mass: (1) the gravitational force between any two objects is F = Gm₁m₂/r², showing direct proportionality to each mass—doubling m₁ doubles F, doubling m₂ doubles F, doubling both quadruples F, (2) this multiplicative relationship means both objects contribute equally to the force magnitude. This principle is crucial for orbital mechanics: doubling a satellite's mass doubles the gravitational force on it, but doesn't change its orbit because acceleration a = F/m stays constant (doubled force divided by doubled mass).
Two students compare gravitational attraction in a simulation where distance stays the same. In Trial 1, the masses are 2 kg and 3 kg, and the force is 6 units. In Trial 2, one mass is doubled to 4 kg while the other stays 3 kg. What happens to the force?
Answer: It becomes 12 units because doubling one mass doubles the force. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that gravitational force depends on both masses multiplicatively: in Trial 1 with masses 2 kg and 3 kg, the force is 6 units; in Trial 2, when one mass doubles from 2 kg to 4 kg (while the other stays 3 kg), the force must double because gravitational force is proportional to each mass—doubling either mass doubles the total force. Choice C is correct because it accurately predicts that doubling one mass doubles the force: if 2 kg × 3 kg gives 6 units, then 4 kg × 3 kg gives 12 units (double the force), demonstrating the proportional relationship where F ∝ m₁m₂. Choice A claims force stays the same when mass changes, ignoring that gravitational force depends on both masses; Choice B suggests force increases by only 3 units (linear addition) rather than doubling; Choice D claims larger mass pulls less, completely contradicting the fundamental principle that more mass creates stronger gravitational force. Understanding gravitational force's dependence on mass: (1) gravitational force between two objects depends on both masses: F ∝ m₁m₂, meaning if you double either mass, you double the force, (2) this explains why Earth (massive) and you (less massive) attract each other with noticeable force, while two people standing near each other (both relatively small masses) experience negligible gravitational attraction. This multiplicative relationship is why massive objects like planets dominate gravitational interactions in their vicinity, and why doubling the mass of either object in a gravitational pair doubles the force between them.
A simulation keeps the distance between two objects the same and keeps one object's mass fixed. Only the other object's mass changes. Changing mass (kg) | Gravitational force (N) 1 | 2 2 | 4 4 | 8 What pattern does the simulation show?
Answer: Gravitational force is proportional to the changing mass (double the mass → double the force). This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: when the changing object's mass doubles from 1 kg to 2 kg (keeping the other object's mass constant), the force doubles from 2 N to 4 N; when mass doubles again from 2 kg to 4 kg, force doubles from 4 N to 8 N—this demonstrates that gravitational force depends on both masses, and the relationship is proportional for each mass individually. Choice A is correct because it accurately identifies the proportional relationship: double the mass → double the gravitational force. Choice B reverses the relationship, claiming force decreases as mass increases when the data clearly show force increasing with mass: 1 kg → 2 N, 2 kg → 4 N, 4 kg → 8 N (all increasing together); Choice C claims mass doesn't affect gravitational force, when the entire dataset demonstrates that mass is the primary factor determining force; Choice D makes an incorrect calculation, claiming quadrupling mass (from 1 to 4 kg) increases force by only 2 N when actually it increases from 2 N to 8 N (increase of 6 N). Understanding gravitational force's dependence on mass: (1) gravitational force between two objects depends on both their masses, following F = Gm₁m₂/r² where G is the gravitational constant, m₁ and m₂ are the masses, and r is the distance between them, (2) keeping one mass and distance constant makes force proportional to the other mass: F ∝ m, (3) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: satellite engineers use this principle to calculate orbital mechanics—doubling a satellite's mass doubles the gravitational force on it, but doesn't change its orbit because acceleration (a = F/m) stays constant when both force and mass double.
A student makes a graph of mass vs. weight for objects on Earth (where $g \approx 10\ \text{N/kg}$ ). The plotted points are (1 kg, 10 N), (2 kg, 20 N), and (4 kg, 40 N). Which description best matches what the graph would look like?
Answer: A straight line through the origin that rises as mass increases. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The data clearly demonstrate proportionality: an object with mass 1 kg has weight 10 N on Earth, 2 kg object has weight 20 N (doubled), 4 kg object has weight 40 N (doubled again)—each time mass doubles, weight doubles, showing the linear proportional relationship that produces a straight line through (0,0), (1,10), (2,20), (4,40). Choice A is correct because it accurately describes a straight line through the origin that rises as mass increases—this is the graphical representation of direct proportionality where weight = 10 × mass, creating a line with slope 10 N/kg passing through the origin. Choice B (horizontal line) would mean weight stays constant regardless of mass, contradicting the data; Choice C (downward slope) suggests weight decreases as mass increases, opposite to reality; Choice D (curve that doubles) misunderstands linear relationships—doubling in height for each kg increase would create an exponential curve, not the straight line that proportionality produces. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) this creates a linear graph because W = 10m is the equation of a straight line with slope 10 and y-intercept 0. Practical implications: engineers use these linear relationships for quick calculations—if they know one data point (like a 100 kg load weighs 1000 N), they can instantly calculate any other weight by simple proportions.
A simple simulation keeps the distance between two objects the same and keeps one object's mass constant. Only the other mass changes. The measured gravitational force is shown. What pattern does the data show?
Answer: The gravitational force is proportional to the changing mass (doubling the mass doubles the force). This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: when Object 2's mass doubles from 1 kg to 2 kg (keeping Object 1's mass constant), the force doubles from some baseline to twice that value; when Object 2's mass doubles again to 4 kg, force doubles again—this demonstrates that gravitational force depends on both masses (each contributes), and the relationship is proportional for each mass individually (both contribute multiplicatively to total force). Choice A is correct because it accurately identifies the proportional relationship: more mass → more gravitational force and correctly interprets the data showing that doubling mass doubles gravitational force. Choice B claims mass doesn't affect gravitational force, when the entire dataset demonstrates that mass is the primary factor determining gravitational force between objects; Choice C reverses the relationship, claiming more mass produces less gravitational force when the data clearly show force increases with mass; Choice D makes prediction violating proportionality: claims doubling mass triples force, when the pattern shows exact doubling. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): 50 kg person weighs 500 N, 100 kg person weighs 1000 N (double mass, double weight), (3) same object has different weights on different planets because g varies with planet mass: Moon (low mass) has g = 1.6 m/s² so you weigh 1/6 of Earth weight (much lighter, easy to jump), Jupiter (high mass) has g = 25 m/s² so you weigh 2.5× Earth weight (much heavier, crushing sensation), and (4) both masses contribute: Earth pulls you down, you pull Earth up (equal forces by Newton's Third Law), but Earth's huge mass means it doesn't noticeably accelerate toward you while you definitely accelerate toward Earth (fall). Practical implications: astronauts feel weightless in orbit not because there's no gravity (gravity still strong at ISS altitude, about 90% of surface gravity), but because they're in continuous free-fall, experiencing the gravitational force but with no normal force from ground to create sensation of weight—understanding that gravity depends on mass helps explain why Moon missions required special low-gravity training (astronauts needed to learn to walk and work in 1/6 Earth gravity where masses feel much lighter but inertia is unchanged).
On Earth, use $g \approx 10\ \text{N/kg}$ . If a backpack has a mass of $3\ \text{kg}$ , what is its weight (gravitational force) on Earth?
Answer: 30 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. For this calculation, we apply the formula W = mg: with mass m = 3 kg and Earth's gravitational field strength g = 10 N/kg, the weight is W = 3 kg × 10 N/kg = 30 N—this demonstrates the direct proportional relationship where tripling the mass (from 1 kg to 3 kg) triples the weight (from 10 N to 30 N). Choice C is correct because it properly applies the weight formula: 3 kg × 10 N/kg = 30 N, showing that a 3 kg backpack weighs 30 N on Earth. Choice A (3 N) incorrectly divides instead of multiplying, or perhaps confuses mass with weight; Choice B (13 N) appears to add mass and g instead of multiplying them; Choice D (300 N) multiplies by 100 instead of 10, perhaps confusing units or decimal placement. Understanding gravitational force's dependence on mass: (1) your weight is the gravitational force Earth exerts on you, calculated as W = mg where m is your mass (in kg) and g is Earth's gravitational field strength (10 m/s²), (2) different mass objects have different weights on Earth because W ∝ m (proportional): a 1 kg book weighs 10 N, a 3 kg backpack weighs 30 N, a 10 kg box weighs 100 N. Practical implications: knowing this relationship helps in everyday situations like estimating whether you can lift something (a 20 kg suitcase weighs 200 N, about 45 pounds), understanding why heavier vehicles need stronger brakes (more mass means more gravitational force pulling downhill), and why weight limits exist on elevators and bridges (structures must support the gravitational force on all the mass they carry).
Two students discuss why a 1 kg object weighs 25 N on Jupiter but only 3.7 N on Mars. Which explanation is best?
Answer: Jupiter has a stronger surface gravity than Mars, so it pulls more strongly on the same mass. This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. For planetary mass variation: Jupiter (more massive than Mars) has stronger g (25 vs 3.7 N/kg), so 1 kg weighs more on Jupiter (25 N) than Mars (3.7 N). Choice A is correct because it properly explains that massive planets have stronger gravity because their large mass creates stronger gravitational fields. Choice D is wrong because it claims Mars pulls more strongly, but data show Mars has weaker gravity. This explains challenges for future Mars colonists adapting to lower gravity.
A simulation keeps distance the same and measures gravitational force while changing only the mass of one object. Mass of object (kg) | Gravitational force (N) 1 | 2 2 | 4 3 | 6 5 | 10 If the mass were increased from 5 kg to 10 kg (distance and the other mass unchanged), what gravitational force would the simulation most likely show?
Answer: 20 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. The simulation results show that increasing either mass increases the gravitational force between two objects: when object's mass doubles from 1 kg to 2 kg, force doubles from 2 N to 4 N; from 2 kg to (approximately) 3 kg, force goes to 6 N—this demonstrates that gravitational force depends on mass and is proportional (force = constant × mass, here constant=2). Extrapolating, from 5 kg (10 N) to 10 kg (double mass) should double force to 20 N. Choice D is correct because it correctly predicts that doubling mass doubles gravitational force. Choice C is wrong because it suggests 15 N, which would violate proportionality (from 5 kg 10 N, double to 10 kg should be 20 N, not 15 N). Understanding this proportionality is key to Newton's law of universal gravitation, where force ∝ m1 × m2.
A person has a mass of $70\ \text{kg}$ . Using $g \approx 10\ \text{N/kg}$ on Earth and $g \approx 1.6\ \text{N/kg}$ on the Moon, which pair best compares the person's weight on Earth and on the Moon?
Answer: Earth: 700 N; Moon: 112 N This question tests understanding that gravitational force depends on mass—specifically, that more massive objects exert (and experience) stronger gravitational forces. Gravitational force is proportional to mass: if you double an object's mass, the gravitational force on it (its weight) doubles; if you triple the mass, the force triples; and this proportional relationship is shown by the equation weight = mass × g (where g is the gravitational field strength, about 10 m/s² on Earth)—a graph of mass vs weight gives a straight line through the origin, demonstrating perfect proportionality. Additionally, more massive planets exert stronger gravitational forces at their surfaces (Jupiter is much more massive than Earth, so surface gravity on Jupiter is much stronger: g = 25 m/s² vs Earth's 10 m/s²), which is why the same object would weigh more on Jupiter than Earth. For planetary mass variation: the Moon has lower mass than Earth, so weaker gravity (g = 1.6 N/kg vs 10 N/kg), meaning a 70 kg person weighs 70 × 1.6 = 112 N on Moon and 70 × 10 = 700 N on Earth. Choice B is correct because it correctly predicts weights using W = mg for each location. Choice A is wrong because it reverses the values, claiming Earth 112 N and Moon 700 N, when weaker Moon gravity should give lower weight. Practical implications: this explains why Apollo astronauts bounded easily on the Moon—their weight was about 1/6 of Earth's, making movement feel lighter despite unchanged mass.

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