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)

Question

BlackTom AI · Accepted Answer

First, restating the problem to ensure understanding: a 100 kg piano is being raised at a constant rate using a frictionless pulley system. We are asked for the force the mover pulls down on the rope, given g = 9.8 m/s^2. The answer choices are 980 N, 245 N, 1960 N, and 490 N.

Option 1: 980 N. This would be the case if the rope directly supports the piano with a single tension T equal to the weight of the piano (mg = 100 kg × 9.8 m/s^2 ≈ 980 N). If the rope is attached to the piano and runs through a single movable or fixed pulley in a way that only one vertical rope segment tension acts upward on the piano, then to lift at constant velocity, the tension must balance the weight, so the pulling force equals 980 N. This aligns with a simple single-rope support scenario.

Option 2: 245 N. This value is one-quarter of the weight (mg/4). It would require a mechanism where four rope segments share the load equally, which is not indicated by a typical simple two-pulley arrangement in the figure. Since the problem mentions a frictionless pulley system but shows only a basic arrangement, mg/4 is not the appropriate balance force here.

Option 3: 1960 N. This is twice the weight (2mg). A force of 1960 N would imply applying a pull greater than the weight by a factor of two, which would accelerate the piano upward or require extra mechanical advantage not present in the described system. It contradicts the constant-rate (zero-acceleration) condition with a simple, non-multiplying pulley setup.

Option 4: 490 N. This equals mg/2, which would occur if the rope provides two upward support forces on the piano (a two-segment support). In a classic two-segment pulley arrangement where the cable runs under a movable pulley attached to the piano, the required pull would indeed be mg/2. However, the given figure does not depict a setup where two rope segments share the load on the piano; it shows a configuration more consistent with a single upward tension balancing the weight.

In summary, understanding the specific pulley configuration is crucial: the diagram corresponds to a setup where a single rope segment supports the piano, requiring a pull equal to the piano’s weight (mg ≈ 980 N). Therefore, the most consistent choice given the figure is 980 N, with the other options representing scenarios that rely on different pulley load-sharing not shown in the image.

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) 单项选择题

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