A massless rope passes over a frictionless pulley with m1 = 4 kg and m2 = 1 kg. Which statement is true about the acceleration?

A massless rope passes over a frictionless pulley with m1 = 4 kg and m2 = 1 kg. Which statement is true about the acceleration?

• A. The lighter mass accelerates downward.
• B. The heavier mass accelerates downward with an acceleration of about 1.96 m/s^2.
• C. The system remains at rest.
• D. The acceleration is 9.8 m/s^2.

Answer: (B)

In this setup, the heavier mass pulls the system downward because the net force is the difference in gravitational forces on the two masses. With a massless rope and a frictionless pulley, the acceleration is shared by both masses and is given by a = (m1 − m2)g / (m1 + m2). Since m1 = 4 kg and m2 = 1 kg, the acceleration magnitude is a = (4 − 1)g / (4 + 1) = 3g/5 ≈ 0.6g ≈ 5.88 m/s^2. The heavier mass moves downward. So the statement that the heavier mass accelerates downward is the directionally correct idea, though the numerical value shown in that option isn’t the actual magnitude. The true acceleration is about 5.9 m/s^2 downward for the heavier mass.

In this setup, the heavier mass pulls the system downward because the net force is the difference in gravitational forces on the two masses. With a massless rope and a frictionless pulley, the acceleration is shared by both masses and is given by a = (m1 − m2)g / (m1 + m2). Since m1 = 4 kg and m2 = 1 kg, the acceleration magnitude is a = (4 − 1)g / (4 + 1) = 3g/5 ≈ 0.6g ≈ 5.88 m/s^2. The heavier mass moves downward.

So the statement that the heavier mass accelerates downward is the directionally correct idea, though the numerical value shown in that option isn’t the actual magnitude. The true acceleration is about 5.9 m/s^2 downward for the heavier mass.