Question

A block has a square base whose sides are 12 cm long and the block itself is 30 cm tall. The block is set on a rough, flat surface where the coefficient of static friction is μ. A horizontal force F is applied to the block at different locations on the block’s vertical sides. It is found that if F is exerted above a height of 24 cm, the block will tip rather than slide, but if F is exerted below the 24 cm height, the block slides rather than tipping. Draw a diagram showing this situation, labeling important lengths and drawing forces acting on the block just before tipping/sliding. Then find the value of μ.

Answer 1

Answer:

μ = 0.25

Explanation:

Draw a free body diagram of the block as it just begins to tip. There are 4 forces:

Weight force mg pulling down at the center,

Normal force N pushing up at the edge,

Friction force Nμ pushing left at the edge,

and applied force F pushing right 24 cm above the edge.

Sum of moments about the edge of the block:

∑τ = Iα

mg (6 cm) − F (24 cm) = 0

F = mg / 4

Sum of forces in the y direction:

∑F = ma

N − mg = 0

N = mg

Sum of forces in the x direction:

∑F = ma

F − Nμ = 0

μ = F / N

μ = (mg / 4) / (mg)

μ = 0.25