A person pulls on a block with a force , at an angle with respect to the

horizontal. The coefficient of friction between the block and the ground is .

For what is the required to make the block slip a minimum?

**Problem Source : Introduction to Classical Mechanics**

The free body diagram can be drawn as below:

What does *slip a minimum* means? It yields that the acceleration of the block . Therefore, the friction force is a kinetic friction but the net force is . With this in mind, we can now construct our equation:

Taking the derivatives of respect to ,

Hence, is the required to make the block slip a minimum.

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