To measure the static friction coefficient between a2.2-kg block and a vertical

Question

To measure the static friction coefficient between a2.2-kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant =457N/m) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. The spring in such a setup is compressed by0.074m. What is the coefficient of static friction?

To measure the static friction coefficient between a2.2-kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant =457N/m) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip downward. The spring in such a setup is compressed by0.074m. What is the coefficient of static friction?

Explanation / Answer

Let:
s be the distance the spring is compressed,
k be the spring constant,
R be the reaction of the wall,
u be the coefficient of static friction.

Resolving horizontally and vertically:
kx = R
mg = F

For equilibrium, he friction force satisfies:
F / R <= u.

Eliminating F and R:
u >= mg / kx.

When the block is about to slip:
u = mg / kx
= (2.2 * 9.81) / (457 * 0.074)
= 0.637

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