A 4-kg block on a frictionless table connected by a string over a pulley to a hanging 2-kg mass. Which equations describe the motion?

A 4-kg block on a frictionless table connected by a string over a pulley to a hanging 2-kg mass. Which equations describe the motion?

• A. For block on table: T = m1 a; For hanging mass: m2 g − T = m2 a
• B. For block on table: T = m1 a; For hanging mass: T − m2 g = m2 a
• C. For block on table: m1 a = T; For hanging mass: m2 g + T = m2 a
• D. For block on table: T = m1 a; For hanging mass: m2 g − T = − m2 a

Answer: (A)

When two masses are connected by a string over a pulley on a frictionless surface, apply Newton's second law to each mass with a consistent direction for the acceleration. For the block on the table, the only horizontal force is the tension pulling toward the pulley, so the net force along that direction is T and it equals m1 times its acceleration to the right: T = m1 a. For the hanging mass, take downward as the positive direction since it moves downward. Gravity pulls downward with m2 g and tension acts upward, opposite to the motion, so the net force in that direction is m2 g − T, which equals m2 a: m2 g − T = m2 a. This combination correctly describes both masses in the system. The other setups mix the forces with the wrong signs or directions (e.g., adding tension to gravity or reversing the assumed acceleration direction), which would not match the actual motion of the masses on a frictionless linkage.

When two masses are connected by a string over a pulley on a frictionless surface, apply Newton's second law to each mass with a consistent direction for the acceleration.

For the block on the table, the only horizontal force is the tension pulling toward the pulley, so the net force along that direction is T and it equals m1 times its acceleration to the right: T = m1 a.

For the hanging mass, take downward as the positive direction since it moves downward. Gravity pulls downward with m2 g and tension acts upward, opposite to the motion, so the net force in that direction is m2 g − T, which equals m2 a: m2 g − T = m2 a.

This combination correctly describes both masses in the system. The other setups mix the forces with the wrong signs or directions (e.g., adding tension to gravity or reversing the assumed acceleration direction), which would not match the actual motion of the masses on a frictionless linkage.