Why the Same Block Needs Three Different Pulls
Two students pull identical 2.0 kg wooden blocks with a spring scale, keeping each block sliding at a steady 0.5 m/s. They record 4 N on smooth tile, 7 N on carpet, and 11 N on sandpaper. Next they set a second 2.0 kg block on top of the first and repeat the carpet trial, reading 14 N. Finally, on smooth tile, they pull a single block with a constant 10 N force and time it: starting from rest, it reaches 6.0 m/s in 2.0 s. A classmate says, 'The 10 N pull means the net force was 10 N, and the steady-speed trials prove that motion always needs a forward force to keep going.'
1. In the three steady-speed trials, what is each spring-scale reading actually measuring, and why must the pull be different on each surface?
Read the worked answer
The block moves at a steady velocity, so its acceleration is zero and the net force on it must be zero. The forward pull is therefore exactly balanced by the backward friction force, which means:
- each spring-scale reading is a measurement of the sliding friction on that surface (4 N, 7 N, 11 N);
- the pull must be different because friction depends on how the surfaces interact - sandpaper grips far more than tile.
Notice that the pull is not what keeps the block moving; it is only what cancels friction. The reading is a way of measuring friction indirectly.
2. The carpet trial with two blocks gave 14 N instead of 7 N. Explain the result using forces, and say whether the reading should be exactly double.
Read the worked answer
Stacking a second identical block doubles the weight pressing down, so the normal force between block and carpet doubles. Because sliding friction scales with the normal force, the friction should roughly double: 7 N -> 14 N, which matches the reading.
Should it be exactly double? Not necessarily:
- the two blocks may not sit as evenly, so pressure is distributed differently;
- carpet fibers compress and vary from spot to spot;
- the scale itself has reading uncertainty.
So the data support 'friction doubles when the pressing force doubles' as a close approximation, not a perfect law from a single trial. Repeating the trial would be needed to know how much of the 14 N is real and how much is scatter.
3. Correct the classmate's two claims using the 10 N tile trial.
Read the worked answer
Claim 1: 'the net force was 10 N.' Wrong. On tile, friction is about 4 N, so the net force is
10 N - 4 N = 6 N forward.
Check with acceleration: a = (6.0 m/s - 0 m/s) / 2.0 s = 3.0 m/s^2. And net force / mass = 6 N / 2.0 kg = 3.0 m/s^2. The two agree, which confirms the friction is still about 4 N even while speeding up.
Claim 2: 'motion needs a forward force.' The steady-speed trials show the opposite. A constant velocity means balanced forces, not the presence of a forward force. If the students stopped pulling the moving block, friction would still act backward, the forces would be unbalanced, and the block would slow down. Motion does not need a force to continue; a change in motion does.