Question

A block with mass m₁ = 8.8 kg is on an incline with an angle θ = 32° with respect to the horizontal.

The spring is replaced with a massless rope that pulls horizontally to prevent the block from moving. What is the minimum tension in the rope?

Now a new block is attached to the string above the first block on the ramp. The new block is made of a different material and has a coefficient of static friction μ = 0.94. What is the minimum mass of the new block to keep the system from accelerating?

Answer 1

us = (8.8 x 9.8 x sin(32) - 142 x 0.14)/(8.8 x 9.8 x cos(32)) = 0.35

1)

Tension, T = (8.8 x 9.8)(sin(32) - 0.35 cos(32))/(cos(32) + 0.35 sin(32)) = 19.2 N

2)

(m + M) x 9.8 x sin(32) = 0.35 x 8.8 x 9.8 x cos(32) + 0.94 x M x 9.8 x cos(32)

Mass, M = 7.59 kg

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