PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A block of mass M rests on a horizontal, frictionless table. One end of a light, inextensible string is attached to the block, and the string passes over a small, friction-less pulley at the edge of the table. The free end of the string supports a movable, light pulley, to which a second light string is attached. The second string loops under the movable pulley and over a second fixed pulley, then supports a hanging mass m as shown in the verbal description below:
• The string attached to the block runs horizontally from the block to the first fixed pulley.
• The string then hangs vertically and supports the movable pulley.
• A separate string is wrapped around the movable pulley; one end is fixed above, the other end passes over a second ceiling-mounted pulley and supports mass m.
Both strings are light and do not slip, and all pulleys are ideal. When the system is released, the block and the hanging mass begin to move.
Take the positive direction of motion for the block to be toward the pulley and the positive direction for the hanging mass to be downward.
(a) Let a be the magnitude of the acceleration of the block. In terms of a, determine the magnitude of the acceleration of the hanging mass.
(b) Derive a symbolic expression for a in terms of M, m, and g.
(c) Obtain a symbolic expression for the tension in the string that is attached to the block.
(d) For M=0.80kg and m=0.30kg, calculate the numerical values of the block’s acceleration and the tension found in part (c).