A block of mass 1.30 kg is pushed up against a wall by a force P that makes an a

Question

A block of mass 1.30 kg is pushed up against a wall by a force P that makes an angle of = 50.0° angle with the horizontal as shown below. The coefficient of static friction between the block and the wall is 0.274 (a) 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.) Pmaxl Pminl- (b) What happens if IPI has a larger value than |Pmaxl? 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 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 12.1° 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.) max Pminl-

Explanation / Answer

given

m = 1.3 kg

P = ?

theta = 50 deg

mu = 0.274

a. for the block to remain stationary

when Pmax axts, the friciton is acting downwards

when Pmin acts, the firciton is acting upwards

hence

from force balance

f = mu*Pmax*cos(theta)

Pmax*sin(theta) = mg + f = mg + mu*Pmax*cos(theta)

Pmax = mg/(sin(theta) - mu*cos(theta)) = 21.6181621342 N

similiarly

Pmin*sin(theta) = mg - mu*Pmin*cos(theta)

Pmin = mg/(sin(theta) + mu*cos(theta)) = 13.535798966 N

b. if P is larger than Pmax, the block slides up

if P is less than Pmin, the block slides down

c. theta = 12.1 deg

Pmin = 26.70611 N

Pmax = NONE

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