Question

A 4 kg block is sliding down a vertical wall while being pushed by an external force as shown in the figure. What is the magnitude of the acceleration of the block (in m/s^2) if the coefficient of kinetic friction between the wall and the block is μₖ = 0.38 and the magnitude of the external force is 11.0 N?

Answer 1

Answer:

6.90 m/s²

Explanation:

Draw a free body diagram. There are 4 forces on the block:

Weight force mg pulling down,

Normal force N pushing right,

Friction force Nμ pushing up (opposing motion),

Applied force F pushing up 30° from the vertical.

Sum of forces in the +x direction:

∑F = ma

F sin θ − N = 0

N = F sin θ

Sum of forces in the -y direction:

∑F = ma

mg − F cos θ − Nμ = ma

mg − F cos θ − Fμ sin θ = ma

mg − F (cos θ + μ sin θ) = ma

Plug in values:

(4 kg) (9.8 m/s²) − (11.0 N) (cos 30° + 0.38 sin 30°) = (4 kg) a

a = 6.90 m/s²