Two objects,A and B,are placed on an inclined plane that can be rotated to different angles of elevation.A starts to slide at twice the angle of elevation that B starts sliding.The respective coefficients for static friction for A and B are μ_A and μ_B.Choose the last answer that is correct. A)μ_B μ_A B)μ_A μ_B C)μ_B = 2 μ_A D)μ_A = 2 μ_B

Question

Two objects,A and B,are placed on an inclined plane that can be rotated to different angles of elevation.A starts to slide at twice the angle of elevation that B starts sliding.The respective coefficients for static friction for A and B are μ_A and μ_B.Choose the last answer that is correct. A)μ_B > μ_A B)μ_A > μ_B C)μ_B = 2 μ_A D)μ_A = 2 μ_B

Quizplus · Accepted Answer

Let the angle of elevation at which B starts sliding be θ. Then, A starts sliding at 2θ. The force of static friction is given by fs ≤ μsN, where N is the normal force acting on the object. The normal force is given by N = mgcosθ, where m is the mass of the object and g is the acceleration due to gravity. The force component parallel to the inclined plane is given by mg sinθ for object B and mg sin(2θ) for object A. For object B, the force of static friction is fs ≤ μsBmgcosθ. The condition for sliding to start is fs = mg sinθ, i.e. μsBmgcosθ = mg sinθ, which gives μsB = tanθ. For object A, the force of static friction is fs ≤ μsAmgcos2θ. The condition for sliding to start is fs = mg sin(2θ), i.e. μsAmgcos2θ = mg sin(2θ), which gives μsA = tanθ/2. Therefore, μsB > μsA, or μ_A > μ_B.

Two Objects,A and B,are Placed on an Inclined Plane That