A wall is tilted by (with vertical axis), and a block is placed against the wall. The block is held in place with a spring (Spring is pushing the block towards the wall). The coefficient of friction between the block and the wall is . Holding the block in place requires that the spring be compressed by . What is the spring constant of the spring in ?
Take .
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Here normal force N = f s p r i n g − m g sin θ
And m g cos θ is component of gravitational force on the block parallel to the surface of the wall.
So to hold the block friction force on the block must be equal (or greater) to m g cos θ .
We know maximum friction force f = μ s N
So,
μ s ( f s p r i n g − m g sin θ ) = m g cos θ
Which implies f s p r i n g = m g sin θ + μ s m g cos θ
And f s p r i n g = k x
So,
k = x m g ( sin θ + μ s cos θ )
=300.909
Rounding this we get 3 0 1 .