Question

A ladder is leaning against a vertical wall, and both ends of the ladder are at...

A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is μ1 = 0.235 and the coefficient of friction between the ladder and the wall is μ2 = 0.153. Determine the maximum angle with the vertical the ladder can make without falling on the ground.

Homework Answers

Answer #1

First consider the forces involved. W: weight N1: normal force from ground N2: normal force from wall F1: normal force from ground F2: normal force from wall The coefficients of friction tell us that F1 < μ1N1 and F2 < μ2N2. The ladder does not move, so the forces in each direction are balanced. N1 + F2 = W N2 = F1 The ladder does not rotate, so the torques are balanced around each end. At the bottom of the ladder the two forces which act at the bottom produce no torque, and likewise at the top. W * L/2 * sin(θ) = N2 * L * cos(θ) + F2 * L * sin(θ) W * L/2 * cos(θ) = N1 * L * cos(θ) + F1 * L * sin(θ) Put all of this together to solve for θ. You should end up with two inequalities, θ < k1 and θ < k2. The smaller restriction is your answer.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A ladder is leaning against a vertical wall, and both ends of the ladder are at...
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is μ1 = 0.125 and the coefficient of friction between the ladder and the wall is μ2 = 0.103. Determine the maximum angle with the vertical the ladder can make without falling on the ground.
A ladder is leaning against a vertical wall, and both ends of the ladder are at...
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is ?1 = 0.115 and the coefficient of friction between the ladder and the wall is ?2 = 0.153. Determine the maximum angle with the vertical the ladder can make without falling on the ground.
A ladder is leaning against a vertical wall, and both ends of the ladder are at...
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is ?1 = 0.165 and the coefficient of friction between the ladder and the wall is ?2 = 0.203. Determine the maximum angle with the vertical the ladder can make without falling on the ground.
A uniform ladder of length L and weight w is leaning against a vertical wall. The...
A uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs = 0.370, determine the smallest angle the ladder can make with the floor without slipping. ° Please show work thank you
A ladder of length 15.0 m and of mass 45.0kg is leaning against a frictionless building...
A ladder of length 15.0 m and of mass 45.0kg is leaning against a frictionless building wall. An85.0-kg person standing on the ladder, 1.00 m from its top end, asks his friend to stand on one of the lower rungs to prevent the ladder from slipping. If the friend’s mass is 65.0 kg, where should he stand to keep the entire system in equilibrium? The coefficient of friction between the ladder and the ground is 0.300, and the angle that...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a 61.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 820-N firefighter has climbed 4.30 m along the ladder from the bottom. Horizontal Force magnitude __N direction - towards the wall or away from the wall? Vertical Force magnitude N direction up or down? (b) If the ladder is just on...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a 57.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 850-N firefighter has climbed 4.20 m along the ladder from the bottom. Horizontal Force magnitude direction Vertical Force magnitude direction (b) If the ladder is just on the verge of slipping when the firefighter is 9.10 m from the bottom, what...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a...
A 16.0-m uniform ladder weighing 490 N rests against a frictionless wall. The ladder makes a 55.0° angle with the horizontal. (a) Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 820-N firefighter has climbed 4.20 m along the ladder from the bottom. Horizontal Force magnitude N direction ---Select--- towards the wall away from the wall Vertical Force magnitude N direction ---Select--- up down (b) If the ladder is just on the...
A uniform 4m long ladder (ML = 50kg) is leaning against the wall at 65° above...
A uniform 4m long ladder (ML = 50kg) is leaning against the wall at 65° above horizontal. There is no friction between the wall and the ladder but there is friction between the ladder and the floor. Determine the normal forces on each end of the ladder and the frictional force on the bottom of the ladder.
A 2.0-m-long, 11-kg ladder is resting against a house wall, making a 35 ∘ angle with...
A 2.0-m-long, 11-kg ladder is resting against a house wall, making a 35 ∘ angle with the vertical wall. The coefficient of static friction between the top of the ladder and the wall the coefficient is 0.00: A. Determine the minimum coefficient of static friction between the ladder feet and the ground needed for the ladder to stay in rest. B. Determine the magnitude of the normal force of the wall on the ladder. C. Determine the magnitude of the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT