A block is being pulled along a rough horizontal surface at a constant speed by a rope. The only forces with components parallel to the surface are tension and friction. Compare the work done by the kinetic friction force on the block,
𝑊
𝑓
𝑘
to the work done by the tension force on the block,
𝑊
𝑇
, as the block is pulled along a displacement of magnitude 10 m. Use the block as the system.

Question

A block is being pulled along a rough horizontal surface at a constant speed by a rope. The only forces with components parallel to the surface are tension and friction. Compare the work done by the kinetic friction force on the block, 
𝑊
𝑓
𝑘
 to the work done by the tension force on the block, 
𝑊
𝑇
, as the block is pulled along a displacement of magnitude 10 m. Use the block as the system.

BlackTom AI · Accepted Answer

We start by identifying the physical setup: a block moving at constant speed on a rough horizontal surface, pulled by a rope with tension along the displacement, and kinetic friction acting opposite the motion. The displacement is 10 m, and the system is the block.
Option 1: W_fk = −W_T. Since the block moves at constant speed, the net work done on the block by all external forces along the displacement must be zero, because the kinetic energy does not change. The tension force does positive work as it points in the direction of motion, while kinetic friction does negative work because it points opposite to the motion. If the magnitudes of these works are equal, their sum is zero, which implies W_fk = −W_T. This makes sense physically: the frictional work exactly cancels the work done by the pulling force in the steady motion scenario.
Option 2: |W_fk| > |W_T|. If this were true, the friction would do more negative work than the positive work from tension, leading to a decrease in kinetic energy and a reduction in speed, contradicting the given condition that speed is constant. Thus this cannot be correct under the stated conditions.
Option 3: W_fk = W_T. This would imply that the frictional work is positive and equal in magnitude to the tension’s work, or that both forces contribute positively to the displacement. Since friction acts opposite to motion, its work cannot be positive; this option contradicts the direction of kinetic friction and the energy accounting for constant speed.
Option 4: |W_fk| < |W_T|. If friction’s magnitude of work were smaller than the tension’s, there would be a net positive work on the block, increasing its kinetic energy and speeding it up, which again conflicts with the stated constant speed. Therefore this option is inconsistent with the scenario.
Overall, the only choice that aligns with constant-speed motion on a rough surface—where the pulling force does positive work and friction does equal-magnitude negative work—is that W_fk equals negative W_T. The reasoning rests on energy conservation for a system with no change in kinetic energy and the opposing directions of the two parallel forces.

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