Equal and Opposite Forces
Help Questions
Middle School Physical Science › Equal and Opposite Forces
A student on a skateboard pushes on a wall with their hands. The student rolls backward, but the wall does not visibly move. Which statement is correct about the forces between the student and the wall while the student is pushing?
The student and the wall push on each other with equal-magnitude forces in opposite directions.
The student pushes on the wall, but the wall does not push back because it doesn’t move.
The forces are in the same direction because both are part of one interaction.
The wall pushes on the student with a larger force because the wall is heavier.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). Even though the wall has thousands of times more mass than the person, the forces are equal in magnitude: when the person pushes the wall with 100 N to the right, the wall pushes the person with exactly 100 N to the left (equal magnitude, opposite direction). The confusion comes from observing that the wall doesn't move while the person might move backward—this difference in motion results from F = ma: the same 100 N force acting on the person (small mass, perhaps 50 kg) gives acceleration a = F/m = 100/50 = 2 m/s² (noticeable motion), while the same 100 N force on the wall (enormous mass, perhaps 10,000 kg) gives a = 100/10,000 = 0.01 m/s² (essentially imperceptible), but the forces themselves are absolutely equal as required by Newton's Third Law. Choice C is correct because it accurately states forces are equal magnitude by Newton's Third Law regardless of mass differences. Choice A incorrectly claims the heavier object exerts more force because of its greater mass, when actually Newton's Third Law requires equal forces regardless of mass. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light ball hits heavy bat, equal forces act (ball on bat = bat on ball), but F = ma means the light ball experiences huge acceleration (big motion change) while heavy bat experiences small acceleration (barely slows)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
A moving baseball hits a bat. The ball rapidly changes direction, and the batter feels the bat jolt in their hands. Which statement best explains why the force of the bat on the ball and the force of the ball on the bat are the same strength?
The bat must exert a larger force because it has more mass than the ball.
Only the ball experiences a force because it is the object that bounces.
Newton’s Third Law: interaction forces come in pairs that are equal in magnitude and opposite in direction.
The ball exerts a smaller force because it changes direction more.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). When the bat hits the ball, we observe that the ball flies away (large motion change) while the bat only slows slightly (small motion change), which might make it seem like the bat exerted more force on the ball than the ball exerted on the bat—but this is incorrect. Both forces are equal (Newton's Third Law guarantees it); the different observable effects come from F = ma applied to different masses: if both experience the same 200 N force but the ball has mass 0.15 kg while the bat has mass 1 kg, the ball's acceleration is a = 200/0.15 ≈ 1,333 m/s² (dramatic motion change) while the bat's is a = 200/1 = 200 m/s² (much smaller motion change), demonstrating that equal forces produce different effects when masses differ. Choice A is correct because it accurately states forces are equal magnitude by Newton's Third Law regardless of mass differences. Choice B incorrectly claims the heavier object exerts more force because of its greater mass, when actually Newton's Third Law requires equal forces regardless of mass. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light ball hits heavy bat, equal forces act (ball on bat = bat on ball), but F = ma means the light ball experiences huge acceleration (big motion change) while heavy bat experiences small acceleration (barely slows)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
Two air-track gliders collide head-on with spring bumpers. Glider 1 has mass 1 kg and Glider 2 has mass 3 kg. During the collision, they push on each other for the same short time interval. Which statement is correct about the interaction forces during the collision?
Each glider exerts an equal-magnitude force on the other, in opposite directions.
The forces are equal only if the gliders have equal masses.
Glider 2 exerts a larger force because it has more mass.
Glider 1 exerts a larger force because it changes speed more.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). Even though Glider 2 has three times more mass than Glider 1, the forces are equal in magnitude: when Glider 1 pushes Glider 2 with 50 N to the right, Glider 2 pushes Glider 1 with exactly 50 N to the left (equal magnitude, opposite direction). The confusion comes from observing that Glider 1 will change velocity much more than Glider 2—this difference in motion results from F = ma: the same 50 N force acting on Glider 1 (mass 1 kg) gives acceleration a = F/m = 50/1 = 50 m/s² (large velocity change), while the same 50 N force on Glider 2 (mass 3 kg) gives a = 50/3 ≈ 16.7 m/s² (smaller velocity change), but the forces themselves are absolutely equal as required by Newton's Third Law. Choice C is correct because it accurately states forces are equal magnitude by Newton's Third Law regardless of mass differences and correctly explains that forces are opposite in direction. Choice A incorrectly claims the heavier object exerts more force because of its greater mass, when actually Newton's Third Law requires equal forces regardless of mass; Choice B incorrectly suggests Glider 1 exerts larger force because it changes speed more, confusing the forces (which are equal) with the accelerations (which differ when masses differ); Choice D incorrectly states forces are equal only if masses are equal, when Newton's Third Law guarantees equal forces regardless of mass ratios. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person).
A $1,\text{kg}$ cart and a $5,\text{kg}$ cart collide. The $1,\text{kg}$ cart’s velocity changes a lot, while the $5,\text{kg}$ cart’s velocity changes only a little. Which conclusion is correct?
The $1,\text{kg}$ cart experienced a greater force because its velocity changed more.
The heavier cart experienced no force because it barely changed motion.
The carts exerted equal-magnitude, opposite-direction forces on each other; the lighter cart had greater acceleration.
The $5,\text{kg}$ cart exerted a greater force because it has more mass.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). Even though the 5 kg cart has five times more mass than the 1 kg cart, the forces are equal in magnitude: when the 1 kg cart pushes the 5 kg cart with 40 N to the right, the 5 kg cart pushes the 1 kg cart with exactly 40 N to the left (equal magnitude, opposite direction). The confusion comes from observing that the 1 kg cart's velocity changes a lot while the 5 kg cart's velocity changes only a little—this difference in motion results from F = ma: the same 40 N force acting on the 1 kg cart gives acceleration a = F/m = 40/1 = 40 m/s² (large velocity change), while the same 40 N force on the 5 kg cart gives a = 40/5 = 8 m/s² (much smaller velocity change), but the forces themselves are absolutely equal as required by Newton's Third Law. Choice C is correct because it accurately states the carts exerted equal-magnitude, opposite-direction forces on each other and correctly explains that the lighter cart had greater acceleration due to its smaller mass. Choice A incorrectly claims the 1 kg cart experienced a greater force because its velocity changed more, confusing the forces (which are equal) with the accelerations (which differ when masses differ); Choice B suggests the 5 kg cart exerted a greater force because it has more mass, violating Newton's Third Law which states action and reaction forces are always equal magnitude; Choice D incorrectly states the heavier cart experienced no force because it barely changed motion, when actually both carts experience equal forces but different accelerations. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light cart hits heavy cart, equal forces act (light on heavy = heavy on light), but F = ma means the light cart experiences huge acceleration (big motion change) while heavy cart experiences small acceleration (barely changes)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
A student swings a bat and hits a baseball. The ball shoots forward and the bat slows down slightly in the student’s hands. Why can the force of the ball on the bat be the same magnitude as the force of the bat on the ball?
Because the forces happen one after the other: first the bat hits the ball, then the ball pushes back.
Because the object that moves farther always experienced the bigger force.
Because Newton’s Third Law says interaction forces come in equal-magnitude, opposite-direction pairs on different objects.
Because the bat is heavier, it must exert a bigger force than the ball.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). When the bat hits the ball, we observe that the ball flies away (large motion change) while the bat only slows slightly (small motion change), which might make it seem like the bat exerted more force on the ball than the ball exerted on the bat—but this is incorrect. Both forces are equal (Newton's Third Law guarantees it); the different observable effects come from F = ma applied to different masses: if both experience the same 200 N force but the ball has mass 0.15 kg while the bat has mass 1 kg, the ball's acceleration is a = 200/0.15 ≈ 1,333 m/s² (dramatic motion change) while the bat's is a = 200/1 = 200 m/s² (much smaller motion change), demonstrating that equal forces produce different effects when masses differ. Choice A is correct because it accurately states forces are equal magnitude by Newton's Third Law regardless of mass differences and correctly identifies them as interaction forces that come in pairs. Choice B incorrectly claims the object that moves farther always experienced the bigger force, confusing the forces (which are equal) with the accelerations (which differ when masses differ); Choice C suggests the heavier object exerts more force because of its greater mass, when actually Newton's Third Law requires equal forces regardless of mass; Choice D misunderstands the timing, suggesting forces happen one after the other when actually action-reaction forces occur simultaneously. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light ball hits heavy bat, equal forces act (ball on bat = bat on ball), but F = ma means the light ball experiences huge acceleration (big motion change) while heavy bat experiences small acceleration (barely slows)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
Two air-track gliders collide with spring bumpers. Glider A has mass $1,\text{kg}$ and Glider B has mass $3,\text{kg}$. During the brief collision, both gliders’ velocities change, but Glider A’s speed changes much more. Which statement best explains this?
Glider B experiences no force because it has more mass.
The heavier glider exerts a larger force, and that is why the lighter glider changes speed more.
Both gliders exert equal and opposite forces on each other, but the smaller mass has a larger acceleration ($F=ma$).
Glider A experiences a bigger force because it changes speed more.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). Even though Glider B has three times more mass than Glider A, the forces are equal in magnitude: when Glider A pushes Glider B with 30 N to the right, Glider B pushes Glider A with exactly 30 N to the left (equal magnitude, opposite direction). The confusion comes from observing that Glider A's speed changes much more than Glider B's—this difference in motion results from F = ma: the same 30 N force acting on Glider A (mass 1 kg) gives acceleration a = F/m = 30/1 = 30 m/s² (large speed change), while the same 30 N force on Glider B (mass 3 kg) gives a = 30/3 = 10 m/s² (smaller speed change), but the forces themselves are absolutely equal as required by Newton's Third Law. Choice C is correct because it accurately states forces are equal magnitude by Newton's Third Law regardless of mass differences and correctly explains that the smaller mass has larger acceleration due to F = ma. Choice A incorrectly claims Glider A experiences a bigger force because it changes speed more, confusing the forces (which are equal) with the accelerations (which differ when masses differ); Choice B suggests Glider B experiences no force because it has more mass, which is absurd—all objects in collisions experience forces; Choice D incorrectly claims the heavier object exerts more force, violating Newton's Third Law which states action and reaction forces are always equal magnitude. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light glider hits heavy glider, equal forces act (light on heavy = heavy on light), but F = ma means the light glider experiences huge acceleration (big motion change) while heavy glider experiences small acceleration (small change)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
A person on a skateboard pushes horizontally on a wall. The person rolls backward. A force sensor on the person’s hands reads $80,\text{N}$ from the wall on the person. What is the force from the person on the wall at that moment?
$80,\text{N}$ in the opposite direction (the person on the wall).
$0,\text{N}$, because the wall does not move.
Less than $80,\text{N}$ because the person is lighter than the wall.
More than $80,\text{N}$ because the wall is stronger than the person.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). The force sensor shows that the wall exerted 80 N on the person, so by Newton's Third Law, the person must exert exactly 80 N on the wall in the opposite direction—the magnitudes are equal (both 80 N) and the directions are opposite, which is exactly what Newton's Third Law predicts. The equal forces confirm that the force the person exerted on the wall equals the force the wall exerted on the person, even though the person rolled backward while the wall remained stationary. Choice B is correct because it accurately states the force is 80 N in the opposite direction, properly applying Newton's Third Law that action-reaction pairs have equal magnitude and opposite direction. Choice A incorrectly claims 0 N because the wall doesn't move, when actually Newton's Third Law requires equal forces regardless of motion—even stationary objects exert equal reaction forces (wall pushes person as hard as person pushes wall); Choice C suggests less than 80 N because the person is lighter, violating Newton's Third Law which states action and reaction forces are always equal magnitude; Choice D incorrectly claims more than 80 N because the wall is stronger, when actually Newton's Third Law requires equal forces regardless of object properties. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when person pushes wall, equal forces act (person on wall = wall on person), but F = ma means the person (small mass) experiences noticeable acceleration (rolls backward) while wall (enormous mass) experiences imperceptible acceleration (doesn't visibly move)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
Two carts collide and stick together. Cart A ($2,\text{kg}$) moves right into Cart B ($4,\text{kg}$) at rest. During the collision, which statement about the forces is correct?
Each cart exerts the same magnitude force on the other, but in opposite directions.
Cart B exerts a larger force on Cart A because Cart A was moving.
Only Cart A experiences a force because it is the one that hits Cart B.
Cart A exerts a larger force on Cart B because Cart B has more mass.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). Even though Cart B has twice the mass of Cart A (4 kg vs 2 kg), the forces are equal in magnitude: when Cart A pushes Cart B with 60 N to the right, Cart B pushes Cart A with exactly 60 N to the left (equal magnitude, opposite direction). The confusion comes from observing different motion changes—this difference in motion results from F = ma: the same 60 N force acting on Cart A (mass 2 kg) gives acceleration a = F/m = 60/2 = 30 m/s² while the same 60 N force on Cart B (mass 4 kg) gives a = 60/4 = 15 m/s² (half the acceleration), but the forces themselves are absolutely equal as required by Newton's Third Law. Choice C is correct because it accurately states that each cart exerts the same magnitude force on the other but in opposite directions, which is exactly what Newton's Third Law requires. Choice A incorrectly claims Cart A exerts a larger force because Cart B has more mass, when actually Newton's Third Law requires equal forces regardless of mass differences; Choice B suggests Cart B exerts a larger force because Cart A was moving, confusing initial motion with force magnitude—Newton's Third Law applies regardless of initial velocities; Choice D incorrectly states only Cart A experiences a force, when Newton's Third Law guarantees both objects in an interaction experience forces. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when lighter cart hits heavier cart, equal forces act (light on heavy = heavy on light), but F = ma means the lighter cart experiences larger acceleration (bigger motion change) while heavier cart experiences smaller acceleration (smaller change)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
During a cart collision, a sensor reports the force on Cart A points left. What must be true about the force Cart A exerts on Cart B at the same moment?
It points left as well, because forces in a collision point in the same direction.
It happens after the force on Cart A, not at the same time.
It points right, and has the same magnitude as the force on Cart A.
It is smaller if Cart B has more mass.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). If the sensor reports that Cart B exerts a force on Cart A pointing left, then by Newton's Third Law, Cart A must exert a force on Cart B that is equal in magnitude but opposite in direction—meaning it points right. This is a direct application of Newton's Third Law: if B pushes A left with force F, then A pushes B right with the same force F, and these forces occur simultaneously as part of the same interaction. Choice B is correct because it accurately states the force points right (opposite to the left force on Cart A) and has the same magnitude, which is exactly what Newton's Third Law requires for action-reaction pairs. Choice A incorrectly claims both forces point in the same direction (left), when action-reaction pairs must be opposite by definition; Choice C suggests the force is smaller if Cart B has more mass, violating Newton's Third Law which states action and reaction forces are always equal magnitude regardless of mass; Choice D misunderstands the timing, claiming the forces happen at different times when actually action-reaction forces occur simultaneously—they are two sides of the same interaction. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light cart hits heavy cart, equal forces act (light on heavy = heavy on light), but F = ma means the light cart experiences huge acceleration (big motion change) while heavy cart experiences small acceleration (barely moves)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.
Force sensors on two colliding carts record the following at the same instant: $F_{\text{A-on-B}} = 12,\text{N}$ right and $F_{\text{B-on-A}} = 12,\text{N}$ left. Which statement best matches Newton’s Third Law?
The cart with the larger mass must be exerting the $12,\text{N}$ force, not the smaller cart.
Because the forces are opposite, one of them must happen first and the other happens later.
The forces are equal and opposite, so they cancel and there is no force on either cart.
The forces are equal in magnitude and opposite in direction, and they act on different carts.
Explanation
This question tests understanding that forces in action-reaction pairs are always equal in magnitude and opposite in direction, even when objects have very different masses or different observable effects. Newton's Third Law states that forces in action-reaction pairs are always equal magnitude and opposite direction—this is not because they balance to zero (they act on different objects so they don't cancel), but because of the fundamental nature of forces: when Object A pushes Object B with force F in one direction, Object B simultaneously pushes Object A with the same force F in the opposite direction, and this equality holds regardless of whether the objects are the same mass, different masses, or even if one object is enormously more massive than the other (like a person pushing a wall, or a ball hitting a massive bat). The force sensors show that during the collision, Cart A exerted force of 12 N to the right on Cart B while Cart B exerted force of 12 N to the left on Cart A—the magnitudes are equal (both 12 N) and the directions are opposite (right vs left), which is exactly what Newton's Third Law predicts. The equal readings confirm that the force Cart A exerted on Cart B equals the force Cart B exerted on Cart A, and these forces act on different carts (A's force acts on B, B's force acts on A). Choice B is correct because it accurately states forces are equal magnitude and opposite in direction, and correctly notes they act on different carts, which is the essence of Newton's Third Law. Choice A incorrectly claims the forces cancel out resulting in no force on either cart, confusing the fact that equal and opposite forces act on different objects (so they don't cancel) with the mistaken idea that they somehow eliminate each other; Choice C suggests the cart with larger mass must be exerting the 12 N force, misunderstanding that both carts exert equal forces regardless of their masses; Choice D incorrectly claims one force happens first and the other later, when actually action-reaction forces occur simultaneously as two aspects of the same interaction. Understanding equal and opposite forces: the magnitudes are always equal (100 N = 100 N, 50 N = 50 N, etc.) and directions are always opposite (right vs left, up vs down) for action-reaction pairs, and this holds true regardless of: (1) object masses (equal forces even if one object 1000× more massive), (2) object materials (rubber ball and steel bat still exert equal forces on each other), (3) whether objects move after (stationary wall still exerts force equal to person pushing it), and (4) whether you can easily observe both effects (wall barely affected by person's push, but force on wall equals force on person). The reason objects often appear to exert different forces is confusion between forces and effects: when light cart hits heavy cart, equal forces act (light on heavy = heavy on light), but F = ma means the light cart experiences huge acceleration (big motion change) while heavy cart experiences small acceleration (barely moves)—forces equal, effects differ, which is why in collisions between very different masses (bug hitting windshield, person pushing building), the lighter object always shows dramatic motion changes while heavier barely affected, yet both experience exactly equal magnitude forces during the interaction, demonstrating Newton's Third Law applies universally regardless of mass ratios.