In an Atwood machine with two masses, which statement about the net external force on the system is correct?

In an Atwood machine with two masses, which statement about the net external force on the system is correct?

• A. The net external force is zero
• B. The net external force equals (m1 + m2) g directed toward the heavier mass
• C. The net external force equals (m1 - m2) g directed toward the heavier mass
• D. The net external force equals (m1 - m2) g directed toward the lighter mass

Answer: (C)

When two masses are connected over a frictionless pulley, the motion is driven by the imbalance in their weights. To find the net external force, sum the forces on both masses along the direction of the motion. Choose a positive direction toward the heavier mass (down on that side, up on the other). Gravity on the heavier mass adds in that direction, giving +m1 g. Gravity on the lighter mass acts downward, which is opposite to the chosen positive direction, giving -m2 g. The rope tensions pull on each mass, but along the whole system these tensions cancel: one tension acts opposite to the motion of the heavy mass, the other aligns with the light mass’s motion, yielding a net zero contribution. Putting it together, the net external force along the direction of motion is m1 g - m2 g = (m1 - m2) g toward the heavier mass. This force drives the acceleration a = [(m1 - m2) g] / (m1 + m2), consistent with Atwood-machine behavior.

When two masses are connected over a frictionless pulley, the motion is driven by the imbalance in their weights. To find the net external force, sum the forces on both masses along the direction of the motion. Choose a positive direction toward the heavier mass (down on that side, up on the other).

Gravity on the heavier mass adds in that direction, giving +m1 g. Gravity on the lighter mass acts downward, which is opposite to the chosen positive direction, giving -m2 g. The rope tensions pull on each mass, but along the whole system these tensions cancel: one tension acts opposite to the motion of the heavy mass, the other aligns with the light mass’s motion, yielding a net zero contribution.

Putting it together, the net external force along the direction of motion is m1 g - m2 g = (m1 - m2) g toward the heavier mass. This force drives the acceleration a = [(m1 - m2) g] / (m1 + m2), consistent with Atwood-machine behavior.