Question

Determine the minimum force P to prevent the 30 kg uniform rod AB from sliding. The contact surface at B is smooth, whereas the coefficient of static friction between the rod and the wall at A is μs= 0.3.

Answer 1

The minimum force P to prevent the rod from sliding is 88.2N.

Step-by-step explanation:

To determine the minimum force P to prevent the uniform rod AB from sliding, we need to consider the forces acting on the rod. There are two forces: the force of gravity and the frictional force at point A. The force of gravity is given by mg, where m is the mass of the rod and g is the acceleration due to gravity. The frictional force can be calculated using the formula fs = μsN, where fs is the frictional force, μs is the coefficient of static friction, and N is the normal force.

Let the length of the rod AB be L. The normal force N is equal to mg, since the rod is in equilibrium. Therefore, the frictional force fs = μsmg. To prevent the rod from sliding, the force P must be greater than or equal to fs. Therefore, we have P ≥ μsmg.

Substituting the given values, P ≥ 0.3 * 30kg * 9.8m/s² = 88.2N. Therefore, the minimum force P to prevent the rod from sliding is 88.2N.