Question

A mass is attached to the free end of the string which is wrapped very tightly around a fixed pulley (radius = 0.125 m; moment of inertia = 0.0352 kg m2 ). When the mass is released it drops and the string unwinds, which causes the pulley to rotate. What is the speed of the mass (m = 0.423 kg) after it has fallen through 125 cm?

A) 1.97 m/s
B) 2.00 m/s
C) 2.28 m/s
D) 4.95 m/s
E) 3.94 m/s

Answer 1

The speed of the mass after falling through 125 cm is 4.95 m/s.

Step-by-step explanation:

To find the speed of the mass after it has fallen through 125 cm, we can use the principle of conservation of energy. The potential energy of the mass when it is at a certain height is converted into kinetic energy as it falls. The formula to calculate the speed is:

speed = sqrt(2gh)

where g is the acceleration due to gravity (9.8 m/s^2) and h is the height (125 cm = 1.25 m). Plugging in these values, we get:

speed = sqrt(2 * 9.8 * 1.25) = 4.95 m/s

Therefore, the correct answer is D) 4.95 m/s.