AP Physics 1 Quiz: Systems And Center Of Mass

20 questions · exam conditions

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Systems And Center Of MassQuestion 1 of 20

A magnet attracts a steel cart on a low-friction track. The magnet is mounted to a second cart; the carts pull toward each other and eventually collide. Define the system as both carts (including the magnet). The magnetic forces between the carts are internal. Assume external horizontal forces are negligible. Initially both carts are at rest. What is the correct description of the center-of-mass motion?

It moves toward the magnet because magnetic forces are stronger than contact forces.

It remains at rest while the carts accelerate toward each other.

It accelerates toward the cart with smaller mass because it speeds up more.

It moves in the direction of whichever cart is initially closer to the center of mass.

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AP Physics 1 Quiz

AP Physics 1 Quiz: Systems And Center Of Mass

Practice Systems And Center Of Mass in AP Physics 1 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 Systems And Center Of Mass, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 1.

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

It moves toward the magnet because magnetic forces are stronger than contact forces.
It remains at rest while the carts accelerate toward each other. (correct answer)
It accelerates toward the cart with smaller mass because it speeds up more.
It moves in the direction of whichever cart is initially closer to the center of mass.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal magnetic forces between the carts cancel in pairs and do not produce net force on the system. With negligible external horizontal forces and initial rest, the center of mass remains at rest as the carts approach. Choice A is incorrect because magnetic forces are internal and cannot move the center of mass without external influence. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 2

A rocket in deep space ejects exhaust gases backward. Define the system as rocket + exhaust gases that have been expelled. Forces between the rocket and the exhaust are internal to this system, and external forces are negligible. Initially the system is at rest. As fuel burns and exhaust is expelled, which statement about the center of mass is correct?

It remains at rest because there is no net external force on the system. (correct answer)
It moves forward because the rocket speeds up.
It moves backward because the exhaust has greater total momentum.
It must stay at the rocket's geometric center because the rocket is symmetric.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces between the rocket and exhaust gases cancel out, preserving the system's total momentum. In deep space with negligible external forces and initial rest, the center of mass remains at rest. Choice B is incorrect because the rocket's forward motion is balanced by the exhaust's backward momentum within the system. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 3

Two identical pucks slide on frictionless ice. They collide and stick together. Choose the system as both pucks together; the contact forces during the collision are internal. There are no external horizontal forces. Before the collision, puck 1 moves east and puck 2 moves west with equal speed. Which statement about the center-of-mass motion is correct?

The center of mass moves east because puck 1 hits first.
The center of mass remains at rest before, during, and after the collision. (correct answer)
The center of mass reverses direction at the instant they stick.
The center of mass moves with the stuck-together pucks because internal forces create net momentum.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces during the collision cancel out and do not affect the center-of-mass velocity. With no external horizontal forces and initial total momentum zero, the center of mass remains at rest throughout. Choice D is incorrect because internal forces cannot create net momentum; the stuck pucks stop, but the center of mass stays put. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 4

Two blocks $m_1$ and $m_2$ rest on a rough horizontal floor and are connected by a light string. A student pulls on block $m_1$ with a constant horizontal force to the right. Take the system boundary to include both blocks and the string. Friction from the floor on each block is external to the system. Which statement about the center-of-mass acceleration is correct?

It depends only on the tension in the string, since tension is the largest force.
It is determined by the net external horizontal force on the two-block system. (correct answer)
It is zero because internal forces (tension) cancel in pairs.
It must point toward the more massive block because the center of mass is closer to it.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces, such as the tension in the string, do not affect the net force on the system. The net external horizontal force includes the pulling force and friction on both blocks, which determines the center-of-mass acceleration. Choice C is incorrect because internal forces like tension do cancel, but the acceleration is due to external forces, not zero unless those are balanced. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 5

Two identical pucks on frictionless ice move toward each other with equal speed and stick together in a perfectly inelastic collision. The system boundary includes both pucks; contact forces during collision are internal, and external horizontal forces are negligible. After they stick, how does the center of mass move?

It remains at rest because the total momentum of the system is zero. (correct answer)
It moves in the direction of the puck that was on the right because it ends up on top.
It accelerates during the collision because internal forces are large.
It moves with the speed of one puck because one puck "wins" the collision.

Explanation: This question examines center-of-mass motion in collisions with no external forces. The motion of the center of mass of a system depends only on the net external force acting on the system. For the two pucks, there is no net external horizontal force on the frictionless ice, and initial total momentum is zero due to equal and opposite velocities. Thus, the center of mass remains at rest after they stick together in the inelastic collision. A common distractor is choice C, which mistakenly claims the center of mass accelerates during the collision due to large internal forces, but internal forces cannot change the center-of-mass velocity. To approach such problems, calculate initial total momentum and use conservation laws when external forces are negligible.

Question 6

A person stands on a skateboard on a rough sidewalk and throws a heavy backpack forward. The system boundary includes the person, skateboard, and backpack; the throw forces are internal, but friction from the ground on the skateboard is external. During the throw, what happens to the system's center-of-mass motion?

It cannot accelerate because internal forces never affect the center of mass.
It accelerates backward because the backpack is thrown forward.
It may accelerate due to the external friction force from the ground. (correct answer)
It stays fixed at the person's torso because that is the system's center.

Explanation: This question tests comprehension of center-of-mass motion when external forces are present. The motion of the center of mass of a system depends only on the net external force acting on the system. In this case, while internal throw forces do not affect the center of mass, the external friction from the rough sidewalk on the skateboard can provide a net force. Therefore, the center of mass may accelerate due to this external friction during the throw. A common distractor is choice A, which incorrectly states that internal forces never affect the center of mass, but overlooks that external forces like friction can cause acceleration. For similar scenarios, identify all external forces and assess their net effect on the system's center of mass.

Question 7

A firework explodes at the top of its flight into two fragments. Define the system as both fragments; the explosion forces are internal, and the only significant external force afterward is gravity downward. Immediately after the explosion, compared to just before, the center-of-mass velocity is:

changed abruptly because internal explosion forces can change the system's center-of-mass velocity.
unchanged at that instant because internal forces cannot change center-of-mass velocity. (correct answer)
redirected toward the larger fragment because it has more mass.
zero because the fragments move in opposite directions.

Explanation: This question tests understanding of center-of-mass motion for systems. The center of mass of a system accelerates only when there is a net external force acting on the system. During the firework explosion, the forces that break it into fragments are internal to the system of both fragments. Internal forces, no matter how strong, cannot change the velocity of the center of mass. After the explosion, gravity remains the only significant external force, continuing to accelerate the center of mass downward as before. Choice A incorrectly claims that internal explosion forces can change center-of-mass velocity, which violates conservation of momentum. To analyze explosive separations, recognize that the center of mass continues on its original trajectory while individual pieces may fly apart in various directions.

Question 8

A person walks from the stern to the bow of a floating boat. Define the system as person + boat; water exerts negligible horizontal force on the boat. As the person walks forward relative to the boat, the system's center of mass:

moves forward because the person's motion is forward.
moves backward because the boat moves backward.
remains at rest (or constant velocity) relative to the shore because net external horizontal force is negligible. (correct answer)
must stay at the boat's geometric center, so it stays fixed in the boat.

Explanation: This question tests understanding of center-of-mass motion for systems. The center of mass of a system accelerates only when there is a net external force acting on the system. In this boat scenario, the system is the person plus boat, and the water exerts negligible horizontal force. As the person walks forward relative to the boat, the boat moves backward relative to the shore due to momentum conservation. These are internal interactions that cannot change the center-of-mass position relative to the shore. Choice A incorrectly focuses only on the person's motion without considering the boat's compensating backward motion. To analyze relative motion within systems, remember that internal forces cause equal and opposite momentum changes that keep the center of mass fixed relative to external references.

Question 9

A cart on a frictionless track carries a spring-loaded launcher that fires a second cart backward; for both carts as the system, what happens to the center of mass?

It accelerates in the direction of the cart launched forward because the spring adds energy.
It remains at rest or moves at constant velocity because the spring force is internal to the system. (correct answer)
It moves toward the cart with the stronger launch because that cart has greater momentum.
It moves to the physical center of the larger cart because centers of mass lie within objects.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When a spring-loaded launcher on one cart fires another cart backward, the spring force is internal to the two-cart system—it acts between system components. The center of mass of a system responds only to net external forces, never to internal forces alone. Since the track is frictionless and no external horizontal forces act on the system, the center of mass remains at rest or moves at constant velocity, unchanged by the spring launch. Choice A incorrectly claims the spring adds energy to change center-of-mass motion, but energy addition doesn't violate momentum conservation—internal forces redistribute momentum within the system without changing total momentum. To solve center-of-mass problems, recognize that internal forces can dramatically change individual motions while leaving center-of-mass motion unchanged.

Question 10

Two ice skaters stand on frictionless ice and push off each other. Define the system as both skaters together; the push forces they exert on each other are internal. A steady wind exerts a horizontal force to the east on both skaters (an external force on the system). Immediately after they push off, the skaters move apart while the wind continues. Which describes the motion of the system's center of mass?

It accelerates east because there is a net external force east. (correct answer)
It remains at the midpoint between the skaters at all times.
It remains at rest because the push forces are equal and opposite.
It accelerates west because the skaters move apart in opposite directions.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces, such as the push between the skaters, cancel out and do not affect the center-of-mass motion. Here, the wind provides a net external force eastward on the system, causing the center of mass to accelerate east. Choice C is incorrect because while the internal pushes are equal and opposite, the external wind force still acts, leading to acceleration. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 11

A person stands on a skateboard on level ground. Define the system as person + skateboard. The person throws a heavy ball forward; the force between the person and the ball during the throw is internal only if the ball is included, but the ball is not in the system. Neglect air resistance, but assume the ground exerts negligible horizontal force on the skateboard. Initially the person and skateboard are at rest. After the ball leaves the person's hands, what happens to the center of mass of the defined system?

It remains at rest because the person and skateboard exert equal and opposite forces.
It moves forward because the ball carries momentum forward.
It moves backward because the ball exerts an external impulse on the system. (correct answer)
It moves forward because the center of mass must stay under the person's feet.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Since the ball is not part of the system, the force it exerts on the person during the throw is external, providing a backward impulse. With negligible other external horizontal forces, this causes the center of mass to move backward after the throw. Choice A is incorrect because the forces between person and skateboard are internal, but the external impulse from the ball causes motion. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 12

Two masses are connected by a light rigid rod and slide on a frictionless horizontal table. The system boundary includes both masses and the rod. A student briefly applies a horizontal force to one mass, then removes it. During the push, the applied force is external to the system; forces in the rod are internal. After the student stops pushing, what happens to the center-of-mass motion of the system?

It immediately stops because internal rod forces cancel the motion.
It continues moving at constant velocity in the direction it had at release. (correct answer)
It accelerates because the masses keep pulling on each other through the rod.
It moves in a circle because the rod constrains the masses.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. After the external push ends, internal forces in the rod cancel and do not change the system's momentum. With no ongoing external forces on the frictionless table, the center of mass continues at constant velocity. Choice C is incorrect because internal forces like rod tension cannot accelerate the center of mass. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 13

On a frictionless horizontal track, two carts $A$ and $B$ are connected by a compressed spring. The system boundary includes both carts and the spring. Initially the carts are at rest. The spring is released and pushes the carts apart; the spring forces on the carts are internal and equal in magnitude and opposite in direction. Neglect air resistance and any contact forces from outside the system. Which statement about the center-of-mass motion of the cart–spring system is correct?

The center of mass accelerates in the direction of the cart with larger mass.
The center of mass remains at rest throughout the motion. (correct answer)
The center of mass moves toward the cart that experiences the larger spring force.
The center of mass moves because internal spring forces do net work on the system.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces, such as the spring forces pushing the carts apart, come in equal and opposite pairs according to Newton's third law and thus do not contribute to the net force on the system. Since the track is frictionless and other external forces are neglected, the net external force is zero, so the center of mass remains at rest. Choice A is incorrect because the center of mass does not accelerate toward the larger mass; internal forces cannot cause such acceleration. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 14

Two ice skaters initially at rest push off each other on nearly frictionless ice. For the system of both skaters, what is true of the center of mass?

It remains at rest because there is no net external horizontal force. (correct answer)
It moves toward the skater who pushes harder.
It moves toward the heavier skater because the center of mass must be inside them.
It accelerates because internal forces act on both skaters.

Explanation: This problem illustrates center-of-mass motion when only internal forces act. The center of mass of a system remains at rest (or moves at constant velocity) when the net external force is zero. The pushing forces between the skaters are internal to the two-skater system. Since the ice is nearly frictionless, there's no significant external horizontal force. The skaters will move apart with momenta that are equal and opposite, but their center of mass stays fixed at its initial position. Choice C incorrectly assumes the center of mass must be located inside one of the objects, but it's actually at a point between them. To analyze such problems, first identify your system boundary, then classify all forces as internal or external to that system.

Question 15

A cart rolls right on a level track and catches a ball dropped vertically into it. The system boundary includes the cart and ball; the catching forces are internal, while the track's friction is negligible and weight/normal cancel vertically. Which statement about the system's center-of-mass motion is correct during the catch?

The center of mass slows down because kinetic energy decreases in an inelastic interaction.
The center of mass continues moving right at constant velocity because net external horizontal force is zero. (correct answer)
The center of mass moves vertically downward because the ball falls into the cart.
The center of mass must be located at the cart's geometric center, so it cannot change.

Explanation: This question probes understanding of center-of-mass during interactions with negligible external horizontal forces. The motion of the center of mass of a system depends only on the net external force acting on the system. In this setup, the system of cart and ball has no net external horizontal force, as friction is negligible and vertical forces cancel. Therefore, the center of mass continues moving to the right at constant velocity during the catch, preserving the initial horizontal momentum. A common distractor is choice A, which incorrectly links the decrease in kinetic energy to slowing of the center of mass, but energy loss in inelastic processes does not affect center-of-mass motion. For transferable strategy, always separate horizontal and vertical components and evaluate net external forces in each direction.

Question 16

Two carts on a horizontal track are connected by a string. A fan mounted on cart 1 blows air that pushes cart 1 to the right; assume the air quickly leaves the system. The system boundary includes both carts only; tension is internal, and the fan's thrust is external to the carts-only system. What happens to the center-of-mass motion of the carts-only system?

It remains unchanged because the string tension is internal and cancels.
It accelerates to the right because there is a net external force on the carts-only system. (correct answer)
It accelerates left because cart 2 pulls back on cart 1 through the string.
It stays at the midpoint between carts regardless of forces.

Explanation: This question tests knowledge of center-of-mass acceleration with external thrusts. The motion of the center of mass of a system depends only on the net external force acting on the system. In this carts-only system, the fan's thrust is external since air leaves the system, providing a net force to the right. Thus, the center of mass accelerates to the right due to this net external force. A common distractor is choice A, which mistakenly claims the center of mass remains unchanged because tension is internal, but overlooks the external nature of the thrust. For similar problems, carefully define the system boundary to classify forces as internal or external accurately.

Question 17

Two students on carts (A heavier than B) start at rest on frictionless level track and push each other apart. The system boundary includes both carts and students; the push forces are internal, and vertical normal and weight forces are external but cancel. After they separate, which statement about the system's center-of-mass motion is correct?

The center of mass accelerates toward the heavier cart because it exerts a larger force.
The center of mass remains at rest because there is no net external horizontal force on the system. (correct answer)
The center of mass moves in the direction of the cart that moves faster.
The center of mass is located at the physical center of cart A, so it stays there.

Explanation: This question assesses understanding of center-of-mass motion in isolated systems. The motion of the center of mass of a system depends only on the net external force acting on the system. In this scenario, the system of both carts and students experiences no net external horizontal force, as the track is frictionless and vertical forces cancel. Therefore, the center of mass, which was initially at rest, must remain at rest even after the students push apart, as internal push forces do not affect the overall center-of-mass motion. A common distractor is choice A, which incorrectly suggests that internal forces can cause the center of mass to accelerate toward the heavier cart, but internal forces cancel out in pairs and do not influence the center-of-mass acceleration. To analyze similar problems, always identify the system boundary and determine the net external force to predict center-of-mass behavior.

Question 18

A ball and Earth interact gravitationally as the ball falls straight down. Define the system as ball + Earth; the gravitational forces between them are internal, and ignore air resistance and other external forces. What happens to the center-of-mass motion of this system?

It accelerates downward because the ball accelerates downward.
It accelerates upward because Earth's acceleration is upward.
It remains at rest (or constant velocity) because there is no net external force on the system. (correct answer)
It must be located at the center of Earth, so it cannot move.

Explanation: This question tests understanding of center-of-mass motion for systems. The center of mass of a system accelerates only when there is a net external force acting on the system. With the system defined as ball plus Earth, the gravitational forces between them are internal forces—the ball pulls Earth up while Earth pulls the ball down with equal magnitude. Since these are the only significant forces and they are internal to the system, there is no net external force. Therefore, the center of mass of the ball-Earth system remains at rest or continues at constant velocity. Choice A incorrectly considers only the ball's motion without recognizing that Earth also accelerates (imperceptibly) toward the ball. To properly analyze gravitational systems, include all interacting objects and recognize that their mutual forces are internal to the complete system.

Question 19

A cart of mass $M$ on a frictionless track carries a smaller block of mass $m$ on top. The block is pushed by the cart's internal spring launcher so that the block slides to the right relative to the cart. Define the system as cart + block + launcher. All contact forces between cart and block are internal to the system; there are no external horizontal forces. What is the correct description of the center-of-mass motion?

It accelerates right because the block moves right relative to the cart.
It remains at rest because the net external horizontal force is zero. (correct answer)
It moves right because the center of mass must follow the block's motion.
It moves left because the cart recoils more than the block moves.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces from the launcher and between cart and block cancel in pairs, producing no net force on the system. Without external horizontal forces, the center of mass remains at rest while the parts move oppositely. Choice A is incorrect because relative motion does not imply center-of-mass acceleration without external forces. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.

Question 20

A small cart on a horizontal track carries a fan that blows air to the left. Define the system as cart + fan + all expelled air. The track is frictionless, and air resistance from the room on the expelled air is negligible. Forces between the fan and the expelled air are internal to the system. Initially the system is at rest. After the fan runs, what happens to the center of mass of the defined system?

It moves right because the cart experiences a thrust force.
It moves left because the expelled air carries momentum left.
It remains at rest because there is no net external horizontal force. (correct answer)
It oscillates back and forth because the air flow is internal.

Explanation: This question tests the concept of center-of-mass motion for a system of particles. The motion of the center of mass of a system is determined solely by the net external force acting on the system, as if all the mass were concentrated at the center of mass and all external forces acted there. Internal forces, such as those between the fan and the expelled air, cancel in pairs and do not change the total momentum of the system. With no net external horizontal force—due to the frictionless track and negligible air resistance—the center of mass remains at rest. Choice B is incorrect because the expelled air's momentum is part of the system, so it balances the cart's motion without moving the center of mass. To solve similar problems, always identify the system boundary and calculate the net external force to determine the center-of-mass acceleration.