Middle School Science Quiz: Forces And Potential Energy
20 questions · exam conditions
0:00
Forces And Potential EnergyQuestion 1 of 20

A student lifts a backpack of mass 5 kg5\,\text{kg} from the floor to a shelf 1.5 m1.5\,\text{m} high at constant speed. Take g≈10 N/kgg \approx 10\,\text{N/kg}.

Which statement correctly describes the work and the change in gravitational potential energy of the backpack?

The student does negative work, and the backpack's gravitational potential energy decreases.
The student does zero work, and the backpack's gravitational potential energy stays the same.
The student does work against gravity, and the backpack's gravitational potential energy increases by about 75 J75\,\text{J}.
Gravity does work on the backpack while it is lifted, so gravitational potential energy increases because of gravity's work.
← Back to quizzes

Middle School Science Quiz

Middle School Science Quiz: Forces And Potential Energy

Practice Forces And 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 Forces And Potential Energy, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Science.

How to use this quiz

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.

All questions

Question 1

A student lifts a backpack of mass 5 kg5\,\text{kg} from the floor to a shelf 1.5 m1.5\,\text{m} high at constant speed. Take g≈10 N/kgg \approx 10\,\text{N/kg}.

Which statement correctly describes the work and the change in gravitational potential energy of the backpack?

  1. The student does negative work, and the backpack's gravitational potential energy decreases.
  2. The student does zero work, and the backpack's gravitational potential energy stays the same.
  3. The student does work against gravity, and the backpack's gravitational potential energy increases by about 75 J75\,\text{J}. (correct answer)
  4. Gravity does work on the backpack while it is lifted, so gravitational potential energy increases because of gravity's work.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position; when you move an object in the force direction (falling downward in direction of gravity), the force does positive work and potential energy decreases (PE converts to KE typically), but when you move opposite to the force (lifting upward against gravity), you do work against the force and potential energy increases (your work is stored as PE = mgh), with the connection W = ΔPE for conservative forces like gravity. For gravitational force and PE in this lifting scenario: the student moves the backpack upward (opposite to downward gravitational force), doing work against gravity equal to mgh = 5 kg * 10 N/kg * 1.5 m = 75 J, which increases the backpack's gravitational PE by 75 J (from floor h=0, PE=0 to shelf h=1.5 m, PE=75 J). Choice C is correct because it properly connects that the student does work against gravity, increasing the backpack's gravitational potential energy by about 75 J. Choice D is wrong because it suggests work by gravity increases PE when actually gravity does negative work during lifting (opposing the motion), and the PE increase comes from the student's work against gravity. The force-PE relationship helps predict motion and understand energy: lifting against gravity stores energy as increased PE, which can later be released as KE if the object falls. Real examples: like raising a book to a shelf requires work against gravity, increasing PE, similar to how water pumped uphill stores gravitational PE for later use in hydroelectric power.

Question 2

A book is moved in three different ways while Earth's gravity acts downward:

  1. lifted straight up by 1 m1\,\text{m},
  2. carried horizontally across a room at the same height,
  3. lowered straight down by 1 m1\,\text{m}.

Which choice correctly describes how gravitational potential energy changes in each case (ignoring air resistance)?

  1. Up: decreases; Horizontal: increases; Down: stays the same.
  2. Up: increases; Horizontal: stays the same; Down: decreases. (correct answer)
  3. Up: stays the same; Horizontal: decreases; Down: increases.
  4. Up: increases; Horizontal: increases; Down: increases.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position; moving upward (against force) increases PE, downward (with force) decreases PE, and horizontally (perpendicular to force) keeps PE the same since height doesn't change. For gravitational PE changes: lifting up 1 m increases height, so PE increases (ΔPE = mg1 m >0); horizontal carry keeps height same, so PE stays the same (Δh=0, ΔPE=0); lowering down 1 m decreases height, so PE decreases (ΔPE = -mg1 m <0). Choice B is correct because it properly connects the movements to PE changes: up increases, horizontal stays the same, down decreases. Choice A is wrong because it confuses the directions: claims up decreases PE when up actually increases PE (against gravity), and horizontal increases when it stays the same (no height change). The force-PE relationship helps predict motion and understand energy: only vertical movements change gravitational PE, as it's height-dependent. Systematic approach: identify if motion changes height (up: +Δh, increases PE; horizontal: Δh=0, same PE; down: -Δh, decreases PE), and recognize no change horizontally because force is vertical.

Question 3

A 2 kg2\,\text{kg} ball is held at three different heights above the ground: Position G at 0 m0\,\text{m}, Position B at 2 m2\,\text{m}, and Position A at 4 m4\,\text{m}. Take g≈10 N/kgg \approx 10\,\text{N/kg}. The gravitational force on the ball points downward. Which statement correctly connects force direction, potential energy, and work?

(Assume gravitational potential energy is U=mghU = mgh with U=0U=0 at the ground.)

  1. Gravitational force points upward toward higher UU, and lifting the ball decreases UU.
  2. Gravitational force points downward toward lower UU, and lifting from 0 m0\,\text{m} to 4 m4\,\text{m} increases UU by 80 J80\,\text{J} (work done against gravity). (correct answer)
  3. Gravitational force points downward, and moving downward increases UU because the force does positive work.
  4. Gravitational force has no relationship to UU, so UU is the same at all three heights.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. When you move an object in the force direction (falling downward in direction of gravity), the force does positive work and potential energy decreases (PE converts to KE typically), but when you move opposite to the force (lifting upward against gravity), you do work against the force and potential energy increases (your work is stored as PE = mgh). The connection between work and PE change is: W = ΔPE (work equals the change in potential energy for conservative forces like gravity, elastic, and electric forces). For gravitational force and PE: Earth's gravitational force points downward (toward Earth's center), and examining potential energy at different heights shows why: at ground level (h=0), gravitational PE = mgh = 0 (minimum—lowest energy position), at 2 m height, PE = 2102 = 40 J (higher energy), at 4 m height, PE = 2104 = 80 J (even higher energy). The force points from high PE toward low PE: from any elevated position, gravity pulls downward toward the ground (toward h=0 where PE is minimum), demonstrating that gravitational force points in the direction of decreasing PE. If you release an object at height, it falls downward (in force direction) and PE decreases: falling from 4 m to ground, ΔPE = 0 - 80 = -80 J (PE decreases by 80 J), and this lost PE converts to kinetic energy (object speeds up gaining KE = 80 J at bottom). Conversely, lifting against gravity (upward, opposite to force) increases PE: lifting from ground to 4 m, you do work W = mgh = 80 J against gravitational force, and this work is stored as increased PE (ΔPE = +80 J). Choice B is correct because it accurately explains that the gravitational force points downward toward lower U, and lifting from 0 m to 4 m increases U by 80 J as work is done against gravity. Choice A is wrong because it reverses the force direction and PE change: gravity points downward (not upward), and lifting increases U (does not decrease it). Choice C reverses the PE change: moving downward (in force direction) decreases U, not increases it. The force-PE relationship helps predict motion and understand energy: objects released from rest accelerate in force direction (gravity makes things fall downward toward lower PE, converting PE to KE). Systematic approach: identify force direction (downward), determine PE at positions (higher at A and B than G), recognize force points toward low PE (G), predict lifting increases PE.

Question 4

A cart is pushed up a frictionless ramp to a higher platform and then released from rest. While it rolls back down, which statement is correct about the direction of the gravitational force and the cart's gravitational potential energy?

  1. As the cart rolls down in the direction of gravity, gravitational potential energy decreases. (correct answer)
  2. As the cart rolls down in the direction of gravity, gravitational potential energy increases.
  3. Gravity points up the ramp because the cart moves down the ramp.
  4. Gravitational potential energy stays the same because gravity is constant.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position; when you move an object in the force direction (falling downward in direction of gravity), the force does positive work and potential energy decreases (PE converts to KE typically). For gravitational force and PE on the ramp: gravity points downward (toward lower height and lower PE), and as the cart rolls down (in the direction of the component of gravity along the ramp), its height decreases, so gravitational PE decreases (converting to KE as it speeds up). Choice A is correct because it accurately explains that as the cart rolls down in the direction of gravity, gravitational potential energy decreases. Choice B is wrong because it states moving in the force direction increases PE, when moving in the force direction decreases PE (force does positive work, releases PE as KE). The force-PE relationship helps predict motion and understand energy: objects released on a ramp accelerate downward, converting PE to KE. Real examples: a skier going downhill gains speed as gravitational PE decreases, demonstrating forces pointing toward lower energy with systems naturally moving toward minimum PE if free to do so (converting PE to KE in the process).

Question 5

Two objects have opposite electric charges (one positive, one negative). A student slowly pulls them farther apart.

Which statement best describes the work and the electric potential energy change during this separation?

  1. The student does work against the electric attraction, so electric potential energy increases. (correct answer)
  2. The student does work in the direction of the electric force, so electric potential energy increases.
  3. The electric force does work that increases electric potential energy as the charges separate.
  4. No work is needed to separate opposite charges, so electric potential energy does not change.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph); for electric forces with opposite charges, they attract (force pulls together), so to separate them, you move against the attractive force, doing work that increases electric PE (for attraction, PE is lower when close, higher when apart). For electric potential energy with opposite charges: the electric force pulls them together (toward smaller separation, lower PE), so pulling apart means the student does work against this attraction, increasing PE (from close, low PE to far, higher PE). Choice A is correct because it accurately explains that the student does work against the electric attraction, so electric potential energy increases. Choice B is wrong because it claims the student does work in the direction of the electric force, but separation is against the attractive force (force direction is together, motion is apart). The force-PE relationship helps predict motion and understand energy: separating opposite charges stores PE, which can be released as KE if they snap back together. Systematic approach: identify force direction (attraction together), determine PE (lower when close), recognize moving against force increases PE, and predict work input stores energy.

Question 6

A pendulum bob is at three positions: Left endpoint (highest), Bottom (lowest), and Right endpoint (highest). Gravity acts downward.

At which position is the gravitational potential energy minimum, and what does the gravitational force tend to do if the bob is slightly displaced from that position?

  1. Minimum at an endpoint; gravity pulls it back toward the endpoint (stable).
  2. Minimum at the bottom; if displaced, gravity produces a restoring effect that tends to bring it back toward the bottom (stable). (correct answer)
  3. Minimum at the bottom; if displaced, gravity pushes it farther away from the bottom (unstable).
  4. Potential energy is the same at all three positions because the force is always downward.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. When you move an object in the force direction (falling downward in direction of gravity), the force does positive work and potential energy decreases (PE converts to KE typically), but when you move opposite to the force (lifting upward against gravity), you do work against the force and potential energy increases (your work is stored as PE = mgh). The connection between work and PE change is: W = ΔPE (work equals the change in potential energy for conservative forces like gravity, elastic, and electric forces). For gravitational force and PE in pendulum: PE minimum at bottom (lowest height), higher at endpoints; if displaced, gravity pulls toward bottom (lower PE), restoring it (stable equilibrium). Choice B is correct because it identifies minimum at bottom and gravity's restoring effect toward bottom (stable). Choice C confuses stability: at minimum, displacement leads to restoring (not pushing away, which is unstable). Stable equilibrium is at PE minimum, where force points toward it. Pendulum at bottom demonstrates stable position.

Question 7

A block attached to a spring is pulled to the right, stretching the spring, and then released. The spring force on the block points left (back toward the relaxed position). As the block moves left (in the direction of the spring force), what happens to the spring's elastic potential energy (PE)?

  1. Elastic PE increases because the block moves in the direction of the force.
  2. Elastic PE decreases because the spring force does work as the spring returns toward its relaxed (lower-PE) length. (correct answer)
  3. Elastic PE stays constant because only kinetic energy changes during motion.
  4. Elastic PE decreases only if an outside agent pulls the block left.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): for springs, the force points toward the relaxed position because elastic PE is lower there (PE=0 at natural length) than when stretched (PE=½kx²>0). For spring force and elastic PE: when stretched to the right (PE > 0), the spring force points left toward relaxed (minimum PE), and as the block moves left (in force direction) after release, the spring does positive work, decreasing elastic PE (converting to KE as it returns to relaxed). Choice B is correct because it properly explains that elastic PE decreases as the block moves in the force direction toward relaxed (lower PE), with the force doing work. Choice A reverses by saying PE increases when moving in force direction (actually decreases), Choice C claims PE constant (but compression/stretch changes PE), and Choice D confuses by requiring outside agent for decrease (but release allows force to decrease PE). The force-PE relationship helps predict motion and understand energy: releasing a stretched spring causes motion in force direction, decreasing PE and increasing KE. Real examples: a rubber band snaps back when released, converting elastic PE to KE as it moves toward lower PE.

Question 8

A 2 kg2\,\text{kg} ball is held at three different heights above the ground: Position G at 0 m0\,\text{m}, Position B at 2 m2\,\text{m}, and Position A at 4 m4\,\text{m}. The gravitational force on the ball points downward. Which statement correctly connects force direction, work, and gravitational potential energy (PE)? (Use g≈10 N/kgg\approx 10\,\text{N/kg}.)

  1. Gravity points upward toward higher PE, so lifting the ball to 4 m4\,\text{m} makes PE decrease by 80 J80\,\text{J}.
  2. Gravity points downward toward lower PE; lifting from 0 m0\,\text{m} to 4 m4\,\text{m} requires 80 J80\,\text{J} of work against gravity and increases PE by 80 J80\,\text{J}. (correct answer)
  3. Gravity points downward, but PE is the same at all heights because the force is constant.
  4. Gravity points downward, so moving downward increases PE because the force does positive work.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. For gravitational force and PE: Earth's gravitational force points downward (toward Earth's center), and examining potential energy at different heights shows why: at ground level (h=0), gravitational PE = mgh = 0 (minimum—lowest energy position), at 2 m height, PE = 2102 = 40 J (higher energy), at 4 m height, PE = 2104 = 80 J (even higher energy), so the force points from high PE toward low PE, and lifting from 0 m to 4 m (against gravity) requires work W = ΔPE = 80 J, increasing PE by 80 J. Choice B is correct because it accurately explains that gravity points downward toward lower PE, and lifting against the force increases PE by the work done (80 J). Choice A reverses the force-PE relationship by claiming gravity points toward higher PE and PE decreases when lifting, while Choice C incorrectly states PE is constant despite height changes, and Choice D wrongly says moving downward increases PE when it actually decreases PE. The force-PE relationship helps predict motion and understand energy: objects released from rest accelerate in the force direction, converting PE to KE, and stable equilibrium is at PE minimum where forces point toward it. Systematic approach: identify force direction (downward), determine PE at positions (increases with height), recognize force points toward lower PE, and calculate ΔPE = mgh for changes.

Question 9

Two objects have the same positive charge, so they repel each other. Consider two separations: Position 1 where they are 2 cm2\,\text{cm} apart, and Position 2 where they are 10 cm10\,\text{cm} apart. The electric force on each charge points away from the other charge. Which statement best describes the electric potential energy (PE) change when the charges move from 2 cm2\,\text{cm} to 10 cm10\,\text{cm}?

  1. Electric PE increases because the charges move in the direction of the force.
  2. Electric PE decreases because the charges move in the direction of the force (toward lower PE). (correct answer)
  3. Electric PE stays the same because electric forces do not do work.
  4. Electric PE decreases only if an outside agent does work against the force while separating them.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): for repelling charges, the electric force pushes them apart because PE is lower when separated than when close together. For electric potential energy: Two positive charges repel each other (electric force pushes them apart), and the PE relationship shows: close together (2 cm apart), high electric PE (repelling charges forced close have energy stored—like compressed spring), far apart (10 cm apart), low electric PE (separated naturally is lower energy for repulsion), and force points from high to low PE (force pushes apart, from close/high-PE toward far/low-PE), so moving from 2 cm to 10 cm (in force direction) decreases PE as the force does positive work. Choice B is correct because it accurately explains that moving in the force direction decreases electric PE (toward lower PE). Choice A wrongly states PE increases when moving in force direction (actually decreases), Choice C claims PE stays the same (but separation changes PE), and Choice D confuses by saying PE decreases only with outside work against force (but here motion is with the force). The force-PE relationship helps predict motion and understand energy: repelling charges accelerate apart when released, converting PE to KE. Systematic approach: identify force (repulsive, apart), determine PE (higher when closer), recognize force points toward lower PE, and predict PE decreases when moving in force direction.

Question 10

Two opposite charges attract each other. Consider two positions: Position Far (large separation) and Position Near (small separation). The electric force on each charge points toward the other charge. If the charges move from Far to Near and are released from rest, which statement is correct?

  1. Electric potential energy (PE) increases because the charges move in the direction of the force.
  2. Electric potential energy (PE) decreases because the charges move in the direction of the force (toward lower PE), and the electric force can increase their kinetic energy. (correct answer)
  3. Electric potential energy (PE) stays constant because electric forces are not related to potential energy.
  4. Electric potential energy (PE) decreases only if an outside agent does work against the force while they move together.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): for attracting charges, the electric force pulls them together because PE is lower when close than when far apart. For electric potential energy: Opposite charges attract (electric force toward each other), and PE is high when far apart (Position Far), low when near (Position Near, minimum for attraction), so force points from high to low PE; if released from Far, they move toward Near (in force direction), electric force does positive work, decreasing PE and increasing KE (they accelerate together). Choice B is correct because it accurately explains PE decreases when moving in force direction toward lower PE, with force increasing KE. Choice A reverses by saying PE increases in force direction (actually decreases), Choice C claims PE constant (but separation changes PE), and Choice D confuses by requiring outside work for decrease (but motion with force decreases PE). The force-PE relationship helps predict motion and understand energy: attracting charges snap together when released, converting PE to KE. Real examples: opposite charges attract toward lower PE, like gravity pulling objects down.

Question 11

A pendulum bob is at three positions: Left endpoint L (highest point), Bottom B (lowest point), and Right endpoint R (highest point). The gravitational force on the bob points straight downward at all positions. Which statement correctly describes potential energy (PE) and equilibrium?

  1. The bottom position B has minimum gravitational PE and is a stable equilibrium position because small displacements create a force component that points back toward B. (correct answer)
  2. The endpoints L and R have minimum gravitational PE and are stable equilibrium positions because the speed is zero there.
  3. Gravitational PE is the same at L, B, and R because gravity is constant.
  4. B is a maximum of gravitational PE, so the bob is unstable there and moves away if released.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. For gravitational force and PE in a pendulum: at bottom B (lowest height), PE is minimum, at endpoints L and R (highest), PE is maximum, and though gravity points straight down everywhere, the net force component along the pendulum path points toward B (down the arc from L or R), making B a stable equilibrium where small displacements create a restoring force back to B (toward lower PE). Choice A is correct because it correctly identifies bottom B as minimum PE and stable equilibrium, with forces pointing back toward it. Choice B misidentifies endpoints as minimum PE (actually maximum), Choice C wrongly says PE same everywhere (but height varies), and Choice D confuses B as maximum (it's minimum). The force-PE relationship helps predict motion and understand energy: stable equilibrium is at PE minimum, where forces point toward it, so displaced pendulum returns to bottom, converting PE to KE then back. Real examples: a ball in a valley stays at bottom (minimum PE, stable), unlike on a hilltop (maximum PE, unstable).

Question 12

A student lifts a 3 kg3\,\text{kg} book straight up from a shelf at 1 m1\,\text{m} to a higher shelf at 3 m3\,\text{m}. The gravitational force on the book points downward. Approximately how much work must the student do against gravity, and how does the book's gravitational potential energy (PE) change? (Use g≈10 N/kgg\approx 10\,\text{N/kg}.)

  1. The student must do 60 J60\,\text{J} of work against gravity, and the book's gravitational PE increases by 60 J60\,\text{J}. (correct answer)
  2. The student must do 60 J60\,\text{J} of work, and the book's gravitational PE decreases by 60 J60\,\text{J}.
  3. The student must do 30 J30\,\text{J} of work against gravity, and the book's gravitational PE increases by 30 J30\,\text{J}.
  4. No work is required because gravity does the work while lifting upward.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. When you move an object opposite to the force (lifting upward against gravity), you do work against the force and potential energy increases (your work is stored as PE = mgh), so for the 3 kg book lifted from 1 m to 3 m (Δh=2 m), work against gravity W = mgh = 3102 = 60 J, increasing PE by 60 J. Choice A is correct because it accurately connects that the student does 60 J of work against gravity, increasing the book's PE by 60 J. Choice B wrongly says PE decreases (actually increases when lifting), Choice C miscalculates Δh as 1 m (it's 2 m, so 60 J not 30 J), and Choice D incorrectly claims no work needed (gravity opposes lifting, so work is required). The force-PE relationship helps predict motion and understand energy: moving against force requires energy input, storing it as increased PE. Systematic approach: identify motion (up against gravity), calculate W = mgh for ΔPE increase.

Question 13

Two objects have the same positive electric charge. They are held a small distance apart and then released. Which statement best matches the force direction and the change in electric potential energy (PE) as they move?

  1. The electric force pulls them together toward lower PE, so PE decreases as the distance gets smaller.
  2. The electric force pushes them apart toward lower PE, so PE decreases as the distance increases. (correct answer)
  3. The electric force is always downward, so PE depends only on height above the ground.
  4. There is no electric force because the charges are the same, so PE stays constant.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases: for two positive charges that repel, PE is high when close together and low when far apart, so the repulsive force points outward (toward greater separation). For electric potential energy with two positive charges: Two positive charges repel each other (electric force pushes them apart), and the PE relationship shows: close together (small distance), high electric PE (repelling charges forced close have energy stored—like compressed spring), far apart (large distance), low electric PE (separated naturally is lower energy for repulsion), and force points from high to low PE (force pushes apart, from close/high-PE toward far/low-PE). When released, they move in the force direction (apart), so: the repulsive force does positive work pushing them apart, electric PE decreases as separation increases (PE converts to KE), and they accelerate away from each other as stored PE is released. Choice B is correct because it accurately states that the electric force pushes them apart toward lower PE and that PE decreases as distance increases. Choice A incorrectly states the force pulls them together when like charges repel (push apart); Choice C incorrectly claims electric force is always downward when electric forces act along the line between charges; Choice D incorrectly claims there's no force when like charges always repel with a force. The force-PE relationship explains repulsion: like charges naturally move apart (toward lower PE), converting stored electric PE into kinetic energy as they accelerate away from each other.

Question 14

A ball sits in a smooth bowl-shaped track. The lowest point of the bowl is position X. A higher point on either side is position Y. Which statement best explains why position X is a stable equilibrium in terms of force direction and potential energy (PE)?

  1. Position X is stable because it has maximum PE, so any small push makes the ball return to X.
  2. Position X is stable because it has minimum PE; if the ball is moved to Y, the force points back toward X (toward lower PE). (correct answer)
  3. Position X is stable because forces point toward higher PE, so the ball is pushed uphill toward Y.
  4. Position X is stable because PE does not depend on position, so the ball stays wherever it is placed.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that stable equilibrium occurs at PE minimum because forces point toward lower PE, causing displaced objects to return. For the bowl-shaped track: Position X at the bottom has minimum height, so gravitational PE = mgh is minimum there. Position Y on either side has greater height, so PE is higher at Y than at X. When the ball is at Y, the component of gravitational force along the track points down the slope toward X (toward lower PE). If the ball is displaced slightly from X to either side, the force points back toward X (the PE minimum), causing the ball to roll back—this defines stable equilibrium. The ball naturally seeks the lowest PE position: released from Y, it rolls toward X (converting PE to KE), passes through X with maximum speed (minimum PE, maximum KE), climbs the other side (converting KE back to PE), and oscillates around the stable equilibrium at X. Choice B is correct because it accurately identifies X as having minimum PE and explains that forces point back toward X (toward lower PE) when the ball is displaced. Choice A incorrectly claims maximum PE makes equilibrium stable when actually minimum PE creates stability; Choice C incorrectly states forces point toward higher PE; Choice D incorrectly claims PE doesn't depend on position in a gravitational field. The force-PE relationship defines stability: stable equilibrium occurs at PE minima where surrounding forces point inward, while unstable equilibrium occurs at PE maxima where surrounding forces point outward.

Question 15

A student carries a backpack at a constant height across a flat hallway. The backpack moves horizontally while gravity pulls downward. What happens to the backpack's gravitational potential energy (PE) during this horizontal motion, and why?

  1. PE increases because the backpack is moving in the direction of motion.
  2. PE decreases because gravity does work during any motion.
  3. PE stays the same because the height doesn't change (motion is perpendicular to gravity). (correct answer)
  4. PE stays the same because gravity is zero when an object moves horizontally.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that gravitational PE = mgh depends only on vertical height h, not on horizontal position. For horizontal motion at constant height: The backpack moves horizontally while maintaining constant height h, so gravitational PE = mgh remains constant (same m, same g, same h). Gravity pulls straight downward while motion is horizontal (perpendicular directions), so the displacement has no component in the gravity direction. Work by gravity = force × displacement in force direction = mg × 0 = 0 (no vertical displacement means no work by gravity). Since no work is done by or against gravity, there's no change in gravitational PE—it stays constant throughout the horizontal motion. Choice C is correct because it accurately states PE stays the same due to constant height, with motion perpendicular to gravity. Choice A incorrectly claims PE increases just because there's motion; Choice B incorrectly states PE decreases when no work is done by gravity; Choice D gives the right answer but wrong reasoning (gravity isn't zero, it just does no work on horizontal motion). The force-PE relationship clarifies: only the vertical component of motion matters for gravitational PE changes—horizontal motion at constant height involves no work by/against gravity and no PE change.

Question 16

A pendulum bob swings. Consider three positions: left endpoint (highest), bottom (lowest), and right endpoint (highest). Ignoring air resistance, which statement correctly describes gravitational force direction and where gravitational potential energy (PE) is minimum?

  1. Gravity points upward, and PE is minimum at the endpoints because the bob stops there.
  2. Gravity points downward, and PE is minimum at the bottom because the height is smallest there. (correct answer)
  3. Gravity points toward whichever endpoint the bob is moving toward, and PE is minimum at the endpoints.
  4. Gravity is zero at the bottom, so PE is maximum at the bottom.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that gravitational force always points downward (toward Earth's center), and gravitational PE = mgh is minimum where height h is smallest. For a pendulum's gravitational PE: The pendulum bob swings between three key positions: left endpoint at maximum height (high h, high PE), bottom at minimum height (lowest h, minimum PE), and right endpoint at maximum height (high h, high PE). Gravity always points straight downward regardless of the bob's position or motion—it doesn't change direction based on where the bob is going. At the bottom position, height is smallest (h_min), so PE = mgh is minimum; at either endpoint, height is largest (h_max), so PE = mgh is maximum. The gravitational force component along the pendulum's path points from high positions toward the bottom (toward lower PE), causing the bob to accelerate toward the bottom from either side. Choice B is correct because it correctly states that gravity points downward and PE is minimum at the bottom where height is smallest. Choice A incorrectly claims gravity points upward; Choice C incorrectly states gravity changes direction based on motion when gravity always points down; Choice D incorrectly claims gravity is zero at bottom and PE is maximum there when actually PE is minimum at the lowest point. The force-PE relationship explains pendulum motion: the bob accelerates toward the bottom (minimum PE) from either side, converting PE to KE on the way down and KE back to PE on the way up.

Question 17

Two objects have opposite electric charges (one positive, one negative). A student pulls them farther apart at a steady speed. Which statement correctly describes the work done by the student and the electric potential energy (PE) change?

  1. The student does work against the attractive electric force, and the electric PE increases. (correct answer)
  2. The student does work in the direction of the attractive electric force, and the electric PE increases.
  3. The student does no work because electric forces do not affect energy, and PE stays the same.
  4. The student does work against the attractive electric force, and the electric PE decreases.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that when you move opposite to the force, you do work against the force and potential energy increases. For opposite charges (attractive force): Opposite charges attract each other, so the electric force pulls them together (toward smaller separation). The PE relationship for attraction is: close together (small distance), low electric PE (attractive charges naturally want to be close—low energy state), far apart (large distance), high electric PE (separated attractive charges have stored energy—like a stretched spring), and force points from high to low PE (force pulls together, from far/high-PE toward close/low-PE). When the student pulls them farther apart: the student moves them opposite to the attractive force direction (force pulls together, student pulls apart), so the student does work against the attractive electric force, and this work is stored as increased electric PE (farther apart = higher PE for attractive charges). Choice A is correct because it accurately states that the student does work against the attractive force and that electric PE increases when attractive charges are pulled apart. Choice B incorrectly claims the student works in the direction of the force when actually pulling apart is opposite to the attractive force; Choice C incorrectly states no work is done and PE stays constant; Choice D contradicts itself by correctly stating work against force but incorrectly claiming PE decreases. The force-PE relationship shows that separating attractive charges requires energy input (work against attractive force), storing energy as increased PE—like stretching a spring stores energy.

Question 18

A 2 kg2\,\text{kg} ball is held at rest at three different heights above the ground: h=0 mh=0\,\text{m}, h=2 mh=2\,\text{m}, and h=4 mh=4\,\text{m}. Ignore air resistance and take g≈10 N/kgg\approx 10\,\text{N/kg}. Which statement correctly connects force direction, work, and gravitational potential energy (PE)?

  1. Gravity points upward toward higher PE, so lifting the ball decreases PE.
  2. Gravity points downward toward lower PE; lifting the ball requires work against gravity and increases PE by ΔPE=mgΔh\Delta PE = mg\Delta h. (correct answer)
  3. Gravity points downward, but moving downward increases PE because the ball is closer to Earth.
  4. Gravity has no relationship to PE, so PE is the same at 0 m0\,\text{m}, 2 m2\,\text{m}, and 4 m4\,\text{m}.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that forces point in the direction where potential energy decreases (toward lower PE, "downhill" on a PE vs position graph): gravitational force points downward because gravitational PE is lower at ground level (h=0, PE=0) than at height (h>0, PE=mgh>0), so gravity points toward the minimum PE position. For gravitational force and PE: Earth's gravitational force points downward (toward Earth's center), and examining potential energy at different heights shows why: at ground level (h=0), gravitational PE = mgh = 0 (minimum—lowest energy position), at 2 m height, PE = (2)(10)(2) = 40 J (higher energy), at 4 m height, PE = 80 J (even higher energy). The force points from high PE toward low PE: from any elevated position, gravity pulls downward toward the ground (toward h=0 where PE is minimum), demonstrating that gravitational force points in the direction of decreasing PE. When lifting the ball upward (against gravity's downward direction), you do work against the gravitational force, and this work is stored as increased PE: lifting from 0 to 2 m requires work W = mgh = 40 J, which becomes the ball's PE at that height. Choice B is correct because it correctly identifies that gravity points downward toward lower PE and that lifting requires work against gravity which increases PE by ΔPE = mgΔh. Choice A reverses the force-PE relationship by claiming gravity points upward toward higher PE when actually gravity always points downward toward lower PE; Choice C correctly states gravity points downward but incorrectly claims moving downward increases PE when moving downward (in gravity's direction) decreases PE; Choice D incorrectly states gravity has no relationship to PE when gravitational PE = mgh directly depends on height due to gravity.

Question 19

A ball rests at the bottom of a smooth bowl. If the ball is pushed slightly up one side and released, it rolls back down.

Which statement best explains why the bottom of the bowl is a stable equilibrium position?

  1. The bottom is a maximum in gravitational PE, so any small push makes the ball return to the maximum.
  2. The bottom is a minimum in gravitational PE, so the force direction from nearby positions is toward the bottom (lower PE). (correct answer)
  3. The bottom is stable because gravity points upward there, keeping the ball in place.
  4. The bottom is stable because potential energy does not depend on position.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship for stable equilibrium is that it occurs at a potential energy minimum, where forces from all nearby positions point back toward the equilibrium position. For a ball in a bowl: the bottom is the lowest point, so it has minimum gravitational PE (PE = mgh with h smallest at bottom); from any position on the bowl's sides, gravity has a component pointing down the slope toward the bottom; this means displaced balls experience a restoring force toward the bottom (the PE minimum), causing them to roll back. The bottom is stable because it's a PE minimum with forces pointing toward it from all directions. Choice B is correct because it properly identifies the bottom as a minimum in gravitational PE and correctly explains that forces from nearby positions point toward the bottom (lower PE)—this is the defining characteristic of stable equilibrium. Choice A incorrectly calls the bottom a PE maximum when it's clearly the minimum (lowest height); Choice C wrongly claims gravity points upward at the bottom when gravity always points downward; Choice D incorrectly states PE doesn't depend on position. The force-PE relationship shows stable equilibrium occurs at PE minima: any small displacement results in a force pointing back toward the minimum, creating a restoring effect that returns the system to equilibrium, like a ball rolling back to the bowl's bottom or a pendulum returning to vertical.

Question 20

A ball falls straight down from a height of 4 m4\,\text{m} to the ground. Ignore air resistance.

Which statement best describes what happens to gravitational potential energy (PE) and the work done by gravity during the fall?

  1. Gravitational PE increases, and gravity does negative work.
  2. Gravitational PE decreases, and gravity does positive work. (correct answer)
  3. Gravitational PE stays the same, and gravity does no work because the force is constant.
  4. Gravitational PE decreases, and gravity does negative work because the ball speeds up.
Explanation: This question tests understanding of the relationship between forces and potential energy—specifically, that forces point toward positions of lower potential energy and work done by or against forces changes PE. The fundamental relationship is that when you move an object in the force direction (falling downward in direction of gravity), the force does positive work and potential energy decreases (PE converts to KE typically). For a ball falling from 4 m to ground: gravitational force points downward throughout the fall, the ball moves downward (in the same direction as gravity), so gravity does positive work: W = mgh = mg(4) > 0, and gravitational PE decreases from PE₁ = mgh = mg(4) at top to PE₂ = 0 at ground, giving ΔPE = -mg(4) < 0. The lost PE converts to kinetic energy as the ball speeds up during the fall, demonstrating PE → KE conversion. Choice B is correct because it accurately states that gravitational PE decreases and gravity does positive work—both force and displacement are downward, making work positive, and height decreases making PE decrease. Choice A incorrectly states PE increases during a fall—PE decreases when moving in force direction; Choice C wrongly claims PE stays the same—PE depends on height which clearly changes; Choice D correctly identifies PE decreases but incorrectly calls the work negative—work is positive when force and displacement are in same direction. The force-PE relationship predicts that objects released from rest accelerate in the force direction (gravity makes things fall downward), converting potential energy to kinetic energy as they move toward positions of lower PE.