Question

the cylinder and pulley turn without friction about stationary horizontal axles that pass through their centers. a light rope is wrapped around the cylinder, passes over the pulley, and has a 3.00 kg box suspended from its free end. there is no slipping between the rope and the pulley surface. the uniform cylinder has mass 5.00 kg and radius 40.0 cm. the pulley is a uniform disk with mass 2.00 kg and radius 20.0 cm. the box is released from rest and descends as the rope unwraps from the cylinder. find the speed of the box when it has fallen 2.50 m.

Answer 1

To find the speed of the box when it has fallen 2.5 m, we can use the concept of conservation of energy. The speed of the box is 7.9 m/s.

Step-by-step explanation:

To find the speed of the box when it has fallen 2.5 m, we can use the concept of conservation of energy. Initially, the box is at rest and all the potential energy is converted into kinetic energy. The potential energy is given by mgh, where m is the mass of the box, g is the acceleration due to gravity, and h is the height. The kinetic energy is given by (1/2)mv^2, where v is the velocity. Equating the two and solving for v, we get:

v = sqrt(2gh)

Plugging in the values, we have:

v = sqrt(2 * 9.8 m/s^2 * 2.5 m)

v = 7.9 m/s