If the tension in the string in figure (6-E3) is 16 N and the acceleration of each block is 0.5 m/s², find the friction coefficients at the two contacts with the blocks.

Question

If the tension in the string in figure (6-E3) is 16 N and the acceleration of each block is 0.5 m/s 2 , find the friction coefficients at the two contacts with the blocks.

Philoid · Accepted Answer

The free body diagram of the given problem is shown above.

From figure (a)

μ₁R + ma = T

μ₁R + 2(0.5) = 16 {R = mg cosθ}

⇒ μ₁(2g) =15

⇒ μ₁ = 0.75

From figure (b)

μ₂R + ma = F − mg sin θ

⇒μ₂mg cos θ + 4 (0.5) = 16 − 4g sin 30°

⇒μ₂ = 0.06

If the tension in the string in figure (6-E3) is 16 N and the acceleration of each block is 0.5 m/s2, find the friction coefficients at the two contacts with the blocks.

If the tension in the string in figure (6-E3) is 16 N and the acceleration of each block is 0.5 m/s², find the friction coefficients at the two contacts with the blocks.