*66.   The person in the drawing is standing on crutches. Assume that the force exerted on each crutch by the ground is directed along the crutch, as the force vectors in the drawing indicate. If the coefficient of static friction between a crutch and the ground is 0.90, determine the largest angle qMAX that the crutch can have just before it begins to slip on the floor.

Consider the relationship of the angles below

The force of the crutch can be broken into components.  The horizontal component of F is really the static friction force keeping the crutch from sliding away from the user.  The vertical component is opposing the person’s weight and is the Normal force.  Using the orientation of the angle q, we have the following

 

 

Max angle implies max static friction

Plug in for N

 

 

 

 

 

 

 

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This page last updated on January 11, 2020