# Physics

posted by .

A ladder 10-m long and weighing 50 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder and the ground.

• Physics -

The upper wall exerts only a normal force on the ladder -- no friction force. The normal force there (F1) is such that
F1*L sin 50 = W*L/2* cos 50
F1 = (1/2)*W tan 50 = 0.596 W
The normal force at the base equals the weight W, since the other contact point is smooth and frictionless. If it is just about to slip, the maximum static friction force at the base (Ff,max) equals the normal force at the top, which I called F1.

Ff,max = mus*W = F1 = W/2 tan 50

mus = F1/W = (1/2) tan 50 = 0.596
is the static friction coefficient

## Similar Questions

1. ### physics

An 9.0 m, 210 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.75, and the ladder makes a 50.0° angle with the ground. How far up the ladder can an 890 N person …
2. ### Physics

A uniform ladder 10.0m long and weighing 50.0N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the …

A painter climbs a ladder leaning against a smooth wall. At a certain height, the ladder is on the verge of slipping. Let the mass of the painter be 69.0 kg, length = 2.80 m, the ladder’s mass to be 21.0 kg, θ = 57.0°, and …
4. ### physics

A painter climbs a ladder leaning against a smooth wall. At a certain height, the ladder is on the verge of slipping. Let the mass of the painter be 85.0 kg, length = 5.80 m, the ladder’s mass to be 37.0 kg, è = 51.0°, and the …
5. ### ap physics b

A uniform ladder 8.09 m long and weighing 201.0 N rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.600, and the ladder makes a 46.0 angle with the ground. How far up the ladder …
6. ### Physics

A uniform ladder of length (L) and weight 100 N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5. Find the minimum angle theta , which the ladder can make …
7. ### phsics

uniform ladder 25 ft long rests against a smooth vertical wall. The ladder weighs 15 Kg. The lower end of the ladder is 15 ft from the wall. A man weighing 80 Kg climbs up the ladder until he is 20 ft from the base of the ladder, (20 …
8. ### Physics

A 7.68 m, 132 kg uniform ladder rests against a smooth wall. The coefficient of static fric- tion between the ladder and the ground is 0.642, and the ladder makes a 48.4◦ angle with the ground. How far up the ladder can a 528 …
9. ### statics/physics

The uniform 10-kg ladder in the figure rests against the smooth wall at B, and the end A rests on the rough horizontal plane for which the coefficient of static friction is 0.3. determine the angle of inclination of the ladder and …
10. ### Physics

A ladder 10-m long and weighing 50 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder and …

More Similar Questions