A piano mover raises a 100 kg piano at a constant rate using a frictionless pulley system, as shown in the diagram below. With roughly what force is the mover pulling down on the rope?

Question

BlackTom AI · Accepted Answer

Because the piano is lifted at constant speed, its acceleration is zero so the net vertical force is zero. The movable pulley attached to the piano is supported by two vertical segments of the same rope, so those two tensions together balance the piano's weight.

1) Relevant concepts
- Newton’s 2nd law in equilibrium: if acceleration a = 0, then ΣF = 0.
- Tension in an ideal (massless, frictionless) rope is the same everywhere along the rope.
- A single movable pulley that has two supporting rope segments provides an upward force equal to 2T, where T is the rope tension (the force the mover applies).

2) Step-by-step reasoning
- Let T be the tension in the rope (the downward pull by the mover).
- The movable pulley attached to the piano is pulled upward by two rope segments, so total upward force = 2T.
- The downward force on the piano is its weight W = mg.

3) Calculations (all intermediate steps)
- Mass m = 100 kg; use g = 9.8 m/s^2.
- Weight W = mg = 100 kg × 9.8 m/s^2 = 980 N.
- Equilibrium: 2T = W → T = W/2 = 980 N / 2 = 490 N.
- Rounding to two significant figures gives approximately 500 N.

4) Why the correct answer is correct
The diagram shows a single movable pulley with two supporting rope segments; therefore the mover only needs to supply half the piano’s weight as tension to keep it moving at constant velocity. That gives T ≈ 490 N ≈ 500 N.

5) Why the other options are incorrect
- 2000 N: about twice the piano’s weight (not needed and inconsistent with the pulley arrangement).
- 250 N: would be correct only if there were four supporting segments (giving 4T = W), which the diagram does not show.
- 1000 N: equals the full weight approximated with g = 10 m/s^2 (would be the pull for a single rope supporting the piano, not a two-segment movable pulley).
- “Depends on the velocity!”: incorrect because for constant velocity (zero acceleration) the required force is determined by equilibrium, not the speed.

6) Conclusion
Therefore the mover pulls with about 500 N, which matches the provided correct answer (500 N).

A piano mover raises a 100 kg piano at a constant rate using a frictionless pulley system, as shown in the diagram below. With roughly what force is the mover pulling down on the rope?Single choice

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A piano mover raises a 100 kg piano at a constant rate using a frictionless pulley system, as shown in the figure. With roughly what force is the mover pulling down on the rope? (take g = 9.8 m/s2)

A piano mover raises a 100 kg piano at a constant rate using a frictionless pulley system, as shown in the figure. With roughly what force is the mover pulling down on the rope? (take g = 9.8 m/s2)

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