Question

Cylinder B is accelerated from rest by weight A. Cylinder weight is 95 lb, and the radius is 2 feet. Neglect the inertia of the pulley using the dynamic equilibrium method to find the acceleration of weight A. [Assume pure rolling for B.]

a) 2 ft/s²
b) 3 ft/s²
c) 4 ft/s²
d) 5 ft/s²

Answer 1

To find the acceleration of weight A, use the dynamic equilibrium method and relate the angular acceleration to the linear acceleration of the cylinder.

Step-by-step explanation:

To find the acceleration of weight A, we can use the dynamic equilibrium method. This method states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force is the tension in the string, which can be found using the weight of cylinder B.

The tension in the string is equal to the weight of cylinder B (95 lb) minus the weight of weight A (unknown) since the two weights are connected by the string.

Since the cylinder is assumed to be in pure rolling motion, we can relate the angular acceleration to the linear acceleration using the formula: a = Rα, where a is the linear acceleration, R is the radius of the cylinder, and α is the angular acceleration.

Therefore, we can find the angular acceleration of the cylinder using the net torque equation: τ = Iα, where τ is the torque, and I is the moment of inertia of the cylinder. Since the inertia of the pulley is neglected, the moment of inertia is equal to the moment of inertia of the cylinder. Finally, we can relate the angular acceleration to the linear acceleration using the formula mentioned earlier to find the linear acceleration of weight A.