Question

A 250-g weight is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwindsAssume that the spool can be treated as a uniform solid cylinder of radius R = 3 cm and mass Ms = 100 g. Find the tension in the thread and the magnitude of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds.

Answer 1

The weight of the object is the force that is causing both objects to accelerate. To determine the acceleration, use the following equation.

Weight = Total relative mass * acceleration
For the object that is tied to the string, its actual mass is its relative mass. When the cylinder is solid, its relative mass is one half of its mass.

Total relative mass = 0.25 + 0.5 = 0.3 kg
Weight = 0.25 * 9.8 = 2.45
2.45 = 0.3 * a
a = 2.45 ÷ 0.3
This is approximately 8.1667 m/s^2

The weight of the object that is tied to the string is causing it to accelerate. The tension is causing it to decelerate. Let’s use this number and the weight of the object that is tied to the string in the following equation to determine the tension.

Weight – Tension = mass * a
2.45 – T = 0.25 * 2.45 ÷ 0.3
T = 2.45 + (0.6125/0.3)
This is approximately 4.491667 N.