An 8.00kg mas is at rest on an incline, the incline is 32.0degrees. The incline

Question

An 8.00kg mas is at rest on an incline, the incline is 32.0degrees. The incline has a rough surface (us=0.375 and uk=0.250).

a) A force F is applied to the mass, parallel to the incline, directed upward. Find the range of values the applied force F can have to keep the block motionless. Determine the Fmin and Fmax values.

b) A force F is applied to the mass horizontal direction, toward the direction up the incline. Find the force F where the motion of the object up the incline is imminent.

PLEASE SHOW ALL WORK :) THANKS

Explanation / Answer

a)

F max = mg*sin(32) + mg*cos(32)*us = 8*9.8*sin(32) + 8*9.8*cos(32)*0.375 = 66.4782843428536 N

Fmin = mg*sin(32) - mg*cos(32)*us = 8*9.8*sin(32) - 8*9.8*cos(32)*0.375= 16.6130562888808 N

b) Fcos(32) = mg*sin(32) + mg*cos(32)*us

=>Fcos(32) = 8*9.8*sin(32) + 8*9.8*cos(32)*0.375

=> F = 78.3897571896969366 N

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