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Consider a block resting on a horizontal plane with a sufficiently large coeffic

ID: 3901748 • Letter: C

Question

Consider a block resting on a horizontal plane with a sufficiently large coefficient of static friction that it does not slip even though a string tied to the upper right corner is pulling directly to the right.
Draw a free-body diagram showing the tension applied to the upper right corner, the gravitational force applied downward to the center of the block (its center of mass), and the plane's normal force upward and frictional force to the left together acting at the center of the bottom surface. All forces have the correct magnitudes and directions. Nevertheless, this free-body diagram is drawn incorrectly.
Why is it incorrect?

Explanation / Answer

The free-body diagram has four arrows pointing up, down, left, and right, all in equal magnitudes (as the block "does not slip," so there is no movement, velocity, or acceleration -- and if there's no acceleration then the net Force in the x direction is zero, meaning the left and right arrows must be equal. Same for the net Force in the y direction, but this is because the block is resting on a horizontal plane, not moving up or down).

Up arrow: Normal Force (F[N] = |F[g]| = m*g)
Down arrow: gravitational Force (F[g] = m*g)
Left: Force due to static friction (f[s] = ?[s]*m*g)
Right: Tension (T = |f[s]| = ?[s]*m*g)

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