A block of mass 2.80 kg is pushed up against a wall by a force that makes an ang

Question

A block of mass 2.80 kg is pushed up against a wall by a force that makes an angle of so angle with the horizontal as shown below. The coefficient of static friction between the block and the wall is 0.300. (a) Determine the possible values for the magnitude of that allow the block to remain stationary. (If there is no maximum, enter NONE in that answer blank.) (b) What happens if ipi has a larger value than O The block slides up the wal O The block does not slide along the wal O The block slides down the wall What happens if iPi has a smaller value than iPminl O The block slides up the wall O The block does not slide along the wall O The block slides down the wall (c) Repeat parts (a) and (b) assuming the force makes an angle of 0-126 with the horizontal. Determine the possible values for the magnitude of that allow the block to remain stationary. (If there is no maximum, enter NONE in that answer blank.) Pminl What happens if ipi has a larger value than P O The block slides up the wall O The block does not slide along the wall o The block slides down the wall What happens if Pi has a smaller value than Pminl? O The block slides up the wall OThe block does not slide along the wall O The block slides down the wall

Explanation / Answer

Given,

m = 2.8 kg ; theta= 50 deg ; us = 0.3

a)In vertical direction

us N + P sin(theta) - mg = 0

along horizontal:

P cos(theta) - N = 0

N = P cos(theta)

putting this in Y direction eqn and solving for P we get

P = mg/sin(theta) +/- us cos(theta)

for max value

P(max) = [2.8 x 9.8/(sin50 - 0.3 x cos50)] = 47.87 N

for min value

P(min) = [2.8 x 9.8/(sin50 + 0.3 x cos50)] = 28.62 N

Hence, P(max) = 47.87 N and P(min) = 28.62 N

b)(i)The block slides up the wall

(ii)The block sides down the wall

c)for max value

P(max) = [2.8 x 9.8/(sin12.6 - 0.3 x cos12.6)] = -367.67 N

for min value

P(min) = [2.8 x 9.8/(sin12.6 + 0.3 x cos12.6)] = 53.71 N

Hence, P(max) = -367.67 N and P(min) = 53.71 N

The block can not slide up the wall

The block slides down the wall

[logically, P(min) = -367.67 N ; P(max) = 53.71 N]

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