Helping a friend move to a new apartment you are loading a washing machine onto

Question

Helping a friend move to a new apartment you are loading a washing machine onto a truck using an 8 ft long plank. The truck bed is 2.5 ft off the ground. The washing machine weighs 130 pounds.

At first you push parallel to the plank with a force of 100 pounds, but the washing machine does
not move.

1) What is the frictional force on the washing machine? Be sure to specify whether this force is directed up the incline or down.

2) If the coefficient of static friction is 0.40 then how much force (in pounds) must you apply to start the machine up the plank?

Provide equations you used and do not just copy answers from similar questions.

Explanation / Answer

the angle made by the plank with horizontal ?= sin-1(2.5/8) = 18.21

along the plank weight component = 130sin(?)= 40.625 pounds downwards

applied force = 100 along the plank upwards

friction force = 100 - 40.625 =59.38 downwards

2)

friciton force = .4*130*cos(?) = 49.4 pounds

force required to start the machine up the plank = 49.4 + 40.625 = 90 punds

I think this method is better of many to do this work ,

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