Question

# A uniform ladder rests against a frictionless wall at an angle of θ = 54.0° with...

A uniform ladder rests against a frictionless wall at an angle of θ = 54.0° with respect to the ground. If the weight of the ladder is WL = 240 N, the length is L = 7.0 m, and the coefficient of static friction between the ladder and the ground is μs = 0.55, determine the distance a man with a weight of WM = 875 N can climb along the ladder before the ladder begins to slip

. ______m

The net vertical force of the system should be zero for equilibrium

so, R - (m+M)g = 0

=> R = 240 + 875 = 1115 N

this is the vertical contact force between the floor and the ladder.

the net horizontal force on the system should also be zero.

So,

Ffriction - S = 0

us(1115) - S = 0

=> S = 613.25 N

this is the horizontal contact force between the ladder and the wall.

now, for the ladder to not slip while the man is climbing, the net torque on the system should also be zero.

So, taking moments about the point of contact of floor and ladder, we get:

R(0)cos54 + 240(L/2)cos54 + 875(x)cos54 - 613.25(L)sin54 = 0

=> 0 + 493.74 + 875(x)cos54 - 3472.907 = 0

=> x = 5.7925 m

so, the man can climb 5.7925 meters along the length of the ladder until it begins to slip.

#### Earn Coins

Coins can be redeemed for fabulous gifts.

##### Need Online Homework Help?

Most questions answered within 1 hours.

##### Active Questions
• A sample is obtained from a population with u=40 and o=6. Which of the following sample...
• In a survey, 11 people were asked how much they spent on their child's last birthday...
• Discussion 7.1: Practice Critical Thinking How well do you understand this material? Reading the material is...
• A credit score measures a​ person's creditworthiness. Assume the average credit score for Americans is 709....
• A Database Administrator (DBA) is play both managerial role and technical role in a modern organization;...
• The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees...