AP Physics 1 Quiz: Systems And Center Of Mass

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.

Question 1

1. It moves toward the magnet because magnetic forces are stronger than contact forces.
2. It remains at rest while the carts accelerate toward each other. (correct answer)
3. It accelerates toward the cart with smaller mass because it speeds up more.
4. 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

1. It remains at rest because there is no net external force on the system. (correct answer)
2. It moves forward because the rocket speeds up.
3. It moves backward because the exhaust has greater total momentum.
4. 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

1. The center of mass moves east because puck 1 hits first.
2. The center of mass remains at rest before, during, and after the collision. (correct answer)
3. The center of mass reverses direction at the instant they stick.
4. 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

1. It accelerates in the direction of the larger cart’s motion because internal forces are unbalanced.
2. It remains at rest or continues at constant velocity, because only internal forces act within the system. (correct answer)
3. It moves toward the cart with greater mass because the center of mass must be inside the heavier object.
4. It oscillates back and forth between the carts as they separate due to the push.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When two students on frictionless carts push off each other, the push forces are internal to the two-cart system—they form an action-reaction pair between system components. According to Newton's laws, the center of mass of a system accelerates only when acted upon by a net external force. Since the system experiences no external horizontal forces (frictionless surface), the center of mass remains at rest or continues at constant velocity. Choice A incorrectly suggests internal forces can accelerate the system's center of mass, which violates conservation of momentum. To solve center-of-mass problems, always identify whether forces are internal or external to your chosen system.

Question 5

1. It depends only on the tension in the string, since tension is the largest force.
2. It is determined by the net external horizontal force on the two-block system. (correct answer)
3. It is zero because internal forces (tension) cancel in pairs.
4. 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 6

1. It decreases because the string’s tension opposes the motion.
2. It increases because stored energy becomes kinetic energy.
3. It remains unchanged because the snapping involves only internal forces. (correct answer)
4. It becomes zero because the pucks separate.

Explanation: This question examines how internal forces affect center-of-mass motion. The center of mass of a system moves according to the net external force only—internal forces have no effect on it. The string tension between the pucks is an internal force within the two-puck system. When the string snaps, this internal force disappears, causing the pucks to change their individual velocities relative to each other. However, on frictionless ice with no external horizontal forces, the center-of-mass velocity must remain unchanged. The pucks may separate or change speeds individually, but their center of mass continues moving right at the same velocity. Choice B incorrectly suggests that energy conversion affects center-of-mass motion. Remember: internal forces can change relative positions and velocities within a system but never alter the center-of-mass velocity.

Question 7

1. It is greater than $g$ because the heavier ball pulls the lighter ball down.
2. It equals $g$ downward because the only significant external force is gravity. (correct answer)
3. It is less than $g$ because internal forces between the balls reduce the net force.
4. It is zero because both balls accelerate equally.

Explanation: This problem tests understanding of center-of-mass acceleration under gravity. The center-of-mass acceleration equals the net external force divided by total mass, regardless of internal forces or individual object motions. For the two-ball system, gravity acts as an external force on both balls, giving each ball a downward acceleration of g. The center of mass, being a weighted average position, must also accelerate downward at g. Any forces between the balls (like air pressure differences) are internal and don't affect center-of-mass acceleration. Choice C incorrectly assumes internal forces can reduce the effect of external forces on the center of mass. When analyzing multi-object systems under gravity, the center of mass always falls with acceleration g (neglecting air resistance), regardless of the objects' masses or interactions.

Question 8

1. The center of mass accelerates upward while the ball is rising.
2. The center of mass remains fixed in space because internal forces cancel.
3. The center of mass accelerates downward due to the external gravitational force. (correct answer)
4. The center of mass moves upward at constant velocity until the ball reaches its peak.

Explanation: This question examines center-of-mass motion under external forces. The center of mass of any system accelerates according to Newton's second law: the net external force divided by the total mass. For the student-skateboard-ball system, gravity is an external force acting downward on all parts of the system. Therefore, the center of mass must accelerate downward at g, regardless of the internal motions (ball going up, student/skateboard recoiling down). The tossing forces between student and ball are internal and cannot affect center-of-mass acceleration. Choice D incorrectly assumes the center of mass follows the ball's motion, but it actually follows a parabolic path like any projectile. When analyzing multi-object systems, remember that internal forces never affect center-of-mass motion—only external forces matter.

Question 9

1. It suddenly stops because the fragments move in opposite directions.
2. It changes to horizontal motion because the fragments move horizontally.
3. It continues as if no explosion occurred, since the explosion forces are internal. (correct answer)
4. It accelerates upward because chemical energy is released.

Explanation: This question tests understanding of center-of-mass motion during internal explosions. The center of mass of a system follows a trajectory determined solely by external forces, regardless of internal interactions. Before the explosion, the firework's center of mass follows a parabolic path under gravity (neglecting air resistance). The explosion forces are internal to the firework system—they're forces between parts of the firework itself. These internal forces cause the fragments to fly apart but cannot change the center-of-mass trajectory. After explosion, the center of mass continues on the same parabolic path it would have followed if no explosion occurred. Choice A incorrectly assumes that opposite motions of fragments affect the center of mass. Remember: internal forces can rearrange mass within a system but never change the system's center-of-mass motion.

Question 10

1. It increases because the spring force adds momentum to the system.
2. It stays constant because only internal forces act horizontally on the system. (correct answer)
3. It becomes zero because the carts move apart in opposite directions.
4. It changes direction to point toward the larger-mass cart.

Explanation: This question tests understanding of center-of-mass motion for systems with internal forces. The center-of-mass velocity of a system changes only when there's a net external force acting on the system. Here, the spring force between the carts is an internal force—it's part of the system itself. Since the track is frictionless, there are no external horizontal forces acting on the two-cart system. The spring may cause the individual carts to accelerate in opposite directions, but these are internal accelerations that don't affect the center of mass. Choice A incorrectly suggests internal forces can add momentum to a system, which violates conservation of momentum. To solve center-of-mass problems, always identify whether forces are internal or external to your chosen system.

Question 11

1. It remains at rest because the total momentum of the system is zero. (correct answer)
2. It moves in the direction of the puck that was on the right because it ends up on top.
3. It accelerates during the collision because internal forces are large.
4. 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 12

1. It cannot accelerate because internal forces never affect the center of mass.
2. It accelerates backward because the backpack is thrown forward.
3. It may accelerate due to the external friction force from the ground. (correct answer)
4. 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 13

1. changed abruptly because internal explosion forces can change the system’s center-of-mass velocity.
2. unchanged at that instant because internal forces cannot change center-of-mass velocity. (correct answer)
3. redirected toward the larger fragment because it has more mass.
4. 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 14

1. moves forward because the person’s motion is forward.
2. moves backward because the boat moves backward.
3. remains at rest (or constant velocity) relative to the shore because net external horizontal force is negligible. (correct answer)
4. 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 15

1. It changes because the explosion provides a large internal impulse.
2. It continues at constant velocity because external horizontal forces on the system are negligible. (correct answer)
3. It stops because the fragments move in opposite directions after the explosion.
4. It moves toward the larger fragment because the center of mass must lie inside the larger piece.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When a firework explodes into fragments, the explosion forces are internal to the fragment system—they're action-reaction pairs between pieces. The center of mass of a system responds only to net external forces, not internal forces. During the brief explosion in midair, external horizontal forces (like air resistance) are negligible compared to the huge internal explosion forces, so the center of mass continues at constant horizontal velocity through the explosion. Choice C incorrectly assumes opposite fragment motions cause the center of mass to stop, but the center of mass depends on the mass-weighted average position, not individual velocities. To analyze explosive separations, recognize that violent internal forces redistribute momentum within the system while total momentum—and thus center-of-mass velocity—remains constant.

Question 16

1. It accelerates toward the astronaut who pushes harder because internal forces can change system motion.
2. It remains at rest or continues at constant velocity because no external forces act on the system. (correct answer)
3. It moves toward the astronaut with smaller mass because that astronaut moves faster.
4. It moves in a circle because the astronauts move away from each other in opposite directions.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When two astronauts push off each other in deep space, the push forces are internal to the two-astronaut system—they form Newton's third law pairs. The center of mass of any system accelerates only in response to net external forces. Since the astronauts are far from other forces in deep space, no external forces act on the system, so the center of mass remains at rest or continues at constant velocity. Choice A incorrectly suggests one astronaut pushing harder creates unbalanced internal forces, but Newton's third law guarantees the forces are always equal and opposite, regardless of who initiates the push. Remember: the absence of external forces means the system's center of mass maintains its initial state of motion, even as components move dramatically relative to each other.

Question 17

1. It changes abruptly at collision because the carts exert large forces on each other.
2. It continues with constant velocity because the collision forces are internal to the system. (correct answer)
3. It becomes located at the geometric midpoint between the carts after they stick.
4. It must stop after collision because kinetic energy decreases.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. During a collision between two carts on a frictionless track, the collision forces are internal to the two-cart system—they're action-reaction pairs between system components. The center of mass of any system accelerates only when acted upon by net external forces. Since the track is frictionless and no external horizontal forces act on the system, the center of mass continues with constant velocity through the collision, regardless of how violently the carts interact. Choice A incorrectly assumes large internal forces can change center-of-mass motion, but Newton's third law ensures internal forces always cancel when considering the whole system. Remember: collisions may dramatically rearrange mass within a system, but they cannot change the system's center-of-mass velocity without external forces.

Question 18

1. It accelerates toward the student because the student provides an applied force on the system.
2. It remains at rest or continues at constant velocity because the rope tension forces are internal. (correct answer)
3. It moves toward the cart that is closer because the center of mass is always between objects.
4. It must move with the faster cart because the center of mass follows the fastest object.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When a student on one cart pulls a rope attached to another cart, the rope tension forces are internal to the two-cart system—they act between system components. The center of mass of a system accelerates only when acted upon by net external forces. Since the carts are on a low-friction surface with negligible external horizontal forces, the center of mass remains at rest or continues at constant velocity. Choice A incorrectly identifies the student's pull as an external applied force, but since the student is part of the system (on one cart), all forces they exert on the other cart are internal. To correctly analyze center-of-mass motion, carefully define your system boundaries—forces are only external if they originate from outside the entire system.

Question 19

1. It stays at rest because external horizontal forces on the system are negligible. (correct answer)
2. It moves toward the faster skater because speed determines center-of-mass location.
3. It accelerates toward the heavier skater because internal forces pull the center of mass.
4. It moves in the direction of the skaters’ separation because the distance between them increases.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When two ice skaters push off each other on frictionless ice, the push forces between them are internal to the two-skater system. The center of mass of any system accelerates only in response to net external forces, not internal forces. Since the ice is frictionless and no external horizontal forces act on the system, the center of mass stays at rest (it was initially at rest when both skaters were stationary). Choice C incorrectly claims internal forces can pull the center of mass toward one skater, but internal forces always sum to zero by Newton's third law. Remember: internal forces can change how mass is distributed within a system but cannot change the system's center-of-mass motion.

Question 20

1. It accelerates in the direction of the cart that moves faster because that cart dominates motion.
2. It remains at rest or moves at constant velocity because the motor’s forces are internal to the system. (correct answer)
3. It moves toward the cart with greater mass because the center of mass is always at that cart’s center.
4. It oscillates because the carts separate, changing the system’s size.

Explanation: This question tests understanding of center-of-mass motion for systems with only internal forces. When an internal motor pushes two connected carts apart along their connecting bar, the motor forces are internal to the two-cart system—they act between system components. The center of mass of any system accelerates only in response to net external forces. Since the track is nearly frictionless with negligible external horizontal forces, the center of mass remains at rest or moves at constant velocity, unaffected by the internal motor forces. Choice A incorrectly suggests the faster cart's motion dominates the center of mass, but center-of-mass motion depends on total system momentum, not individual speeds. Remember: internal mechanisms can dramatically rearrange a system's configuration, but without external forces, they cannot change the center-of-mass motion.