Give some numericals of friction
Answers
Friction Problems
Problem # 1
A block of mass M = 10 kg is sitting on a surface inclined at angle θ = 45°. Given that the coefficient of static friction is μs = 0.5 between block and surface, what is the minimum force F necessary to prevent slipping? What is the maximum force F that can be exerted without causing the block to slip?
Problem # 2
In the previous problem use θ = 15°. What is the maximum force pushing down the incline so that the block doesn't slip? What is the maximum force pushing up the incline so that the block doesn't slip?
Problem # 3
A conveyor is dumping sand onto a cone shaped pile. Given that the coefficient of static friction between the sand grains is μs, what is the maximum angle θ
Problem # 4
A uniform ladder of length L is leaning against the side of a building, as shown. A person of mass m = 75 kg is standing on it. The mass of the ladder is M = 10 kg. The coefficient of static friction between the ground and ladder is μs1 = 0.5, and the coefficient of static friction between the wall and ladder is μs2 = 0.3. What is the minimum angle θ so that the ladder doesn't slip?
Problem # 5
Two boards are bolted together with two bolts, as shown. The squeeze force between the boards is 500 lbs. If the shear strength of each bolt is 5000 lbs and the coefficient of static friction between the boards is μs = 0.5, what is the maximum force F that can be applied to the boards and not pull them apart?
Problem # 6
A 50 kg crate is being pushed on a horizontal floor at constant velocity. Given that the coefficient of kinetic friction between crate and floor is μk = 0.1, what is the push force F? (Answer: 49 N)
Problem # 7
In the previous problem we are given that the coefficient of static friction between crate and floor is μs = 0.2. What is the minimum force F to overcome friction with the floor? (Answer: 98 N)
Problem # 8
Two children throw a rope over a tree branch and hang off each end. The children have a mass of 40 kg and 50 kg. What is the minimum coefficient of static friction between rope and tree branch so that the rope doesn't slip? To solve this consider the general equation T2 = T1eμθ, where T1 and T2 are the rope tensions on the two ends (with T2 > T1), μ is the coefficient of static friction between rope and tree branch, and θ is the angle of contact between rope and branch, in radians. For example, if the rope wraps completely around the branch then the angle θ = 2π.
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