Question

The beam AB has a negligible mass and thickness and is subjected to a uniformly distributed loading. It is supported at one end by a pin at A and at the other end by the post BC. The post mass is having a mass of 100 kg and negligible thickness. Determine the two coefficients of static friction at B and at C so that when the magnitude of the applied force is increased to P= 200 kN, the post slips at both B and C simultaneously.

a) (mu_B = 0.2, mu_C = 0.3)
b) (mu_B = 0.3, mu_C = 0.2)
c) (mu_B = 0.4, mu_C = 0.5)
d) (mu_B = 0.5, mu_C = 0.4)

Answer 1

To determine the coefficients of static friction at B and C, we analyze the forces and moments acting on the beam and post BC. By equating the moments about point A, we can find the maximum normal force at both B and C, which allows us to calculate the coefficients of static friction. The correct coefficients of static friction are mu_B = 0.3 and mu_C = 0.2.

Step-by-step explanation:

To determine the two coefficients of static friction at B and C, we need to consider the forces acting on the beam and post BC. When the magnitude of the applied force is increased to P = 200 kN, the post slips at both B and C simultaneously, indicating that the frictional force at both B and C reaches its maximum static value.

The frictional force can be calculated using the equation F_friction = mu * N, where mu is the coefficient of static friction and N is the normal force. Since the post starts to slip, the frictional force at both B and C is equal to mu * N_max, where N_max is the maximum value of the normal force.

Therefore, to find the coefficient of static friction, we need to find the maximum normal force at both B and C, which can be determined by equating the moment about point A for the beam and the post. With the given information, the correct coefficients of static friction are mu_B = 0.3 and mu_C = 0.2.