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Chapter 13: Problem 46

Blocks \(A\) and \(B\) each have a mass \(m\). Determine the largest horizontal force \(\mathbf{P}\) which can be applied to \(B\) so that \(A\) will not move relative to \(B\). All surfaces are smooth.

Short Answer

Expert verified
The largest horizontal force that can be applied to block B so that block A will not move relative to block B is equal to the weight of block A, which is \(mg\).

Step by step solution

01

Calculate the Weight of the Blocks

The weight of each block is \(mg\), where \(m\) is the mass of the block and \(g\) is the acceleration due to gravity.
02

Determine the Frictional Force

Since all surfaces are smooth, the frictional force between the two blocks is zero. So, the force \(P\) applied on block B should be such that block A does not move relative to block B. This means P is less than or equal to the weight of A, \(mg\).
03

Formulate the Condition for A to Not Move

For block A to not move relative to block B when force P is applied, P should not exceed the weight of block A. Therefore, the largest force P that can be applied to B so that A doesn't move is \(P \leq mg\).

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Most popular questions from this chapter

The forked rod is used to move the smooth 2-lb particle around the horizontal path in the shape of a lima莽on, \(r=(2+\cos \theta)\) ft. If \(\theta=\left(0.5 t^{2}\right)\) rad, where \(t\) is in seconds, determine the force which the rod exerts on the particle at the instant \(t=1\) s. The fork and path contact the particle on only one side.

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