Please help, Im completely lost Need help with B and C. thank you! Painters at W

Question

Please help, Im completely lost

Need help with B and C. thank you!

Painters at Work

A uniform ladder 5.10  m long rests against a frictionless, vertical wall with its lower end 2.80  m from the wall. The ladder weighs 159  N . The coefficient of static friction between the foot of the ladder and the ground is 0.390. A painter weighing 741  N climbs slowly up the ladder.

Part A

What is the maximum frictional force that the ground can exert on the ladder at its lower end?

351

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Correct

Part B

What is the actual size of the frictional force when the painter has climbed 1.1583  m along the ladder?

279.9

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Incorrect; Try Again; 8 attempts remaining

Part C

How far along the ladder can the painter climb before the ladder starts to slip?

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351

Explanation / Answer

Here ,

let the angle of ladder with floor is theta

theta = arccos(2.80/5.1) = 56.7 degree

part A)

Normal force from the ground , N1 = Wladder + Wpainter

N1 = 741 + 159

N1 = 900 N

maximim frictional force = u * N1

maximim frictional force = 0.390 * 900

maximim frictional force = 351 N

part B)

when the painter is at 1.1583 m

let the normal force from the wall is N2

balancing the moment about the ground support

N2 * 5.1 * sin(56.7 degree) - 741 * 1.1583 * cos(56.7 degree) - 159 * 5.1/2 * cos(56.7 degree) = 0

solving

N2 = 162.77 N

in horizontal direction

frictional force = N2

frictional force = 162.77 N

c)

let the maximum he can climb is x

as maximum N2 = 351 N

351 * 5.1 * sin(56.7 degree) - 741 * x* cos(56.7 degree) - 159 * 5.1/2 * cos(56.7 degree) = 0

solving for x

x = 3.13 m

maximum he can climb to 3.13 m

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