A block of mass 3.45 kg is pushed up against a wall by a force P that makes an a

Question

A block of mass 3.45 kg is pushed up against a wall by a force P that makes an angle of theta = 50.0 degree angle with the horizontal as shown below. The coefficient of static friction between the block and the wall is 0.251. Determine the possible values for the magnitude of P that allow the block to remain stationary. (If there is no maximum, enter NONE in that answer blank.) What happens if |P| has a larger value than |Pmax|? The block slides up the wall. The block does not slide along the wall. The block slides down the wall. What happens if |P| has a smaller value than |Pmin|? The block slides up the wall. The block does not slide along the wall. The block slides down the wall. Repeat parts (a) and (b) assuming the force makes an angle of theta = 13.3 degree with the horizontal. Determine the possible values for the magnitude of P that allow the block to remain stationary. (If there is no maximum, enter NONE in that answer blank.) What happens if |P| has a larger value than |Pmax|? The block slides up the wall. The block does not slide along the wall. The block slides down the wall. What happens if |P| has a smaller value than |Pmin|? The block slides up the wall. The block does not slide along the wall. The block slides down the wall.

Explanation / Answer

For maximum value:

Psin(theta) = uPcos(theta) + mg

Solving we get

P = mg/(sin(theta) - ucos(theta))

Pmax = 3.45*9.8/(sin 50 - .251*cos50) = 55.91 N

For Pmin = 3.45*9.8/(sin50 + .251cos50) = 36.45 N

If it has largeer value it will sldie up

If it has lower value it will fall down.

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