The descending pulley has a radius R and mass M.Find the acceleration of block of mass m placed, on the smooth surface and connected with another light pulley.
To find the acceleration of the block, we can start by analyzing the forces acting on the system.
1. On the descending pulley:
- Force of gravity: F_gravity = M * g (where g is the acceleration due to gravity)
2. On the block:
- Force of gravity: F_gravity_block = m * g
- Tension in the string: Tension (T)
Assuming there is no friction between the block and the smooth surface, the net force acting on the block is given by:
F_net = F_gravity_block - T
Since the block is connected to the descending pulley, the tension T is equal to the tension in the string supporting the pulley. Therefore, we have T = M * g.
Substituting this back into the equation for F_net, we get:
F_net = m * g - M * g
Using Newton's second law of motion (F = m * a, where F is the net force and a is the acceleration), we can find the acceleration of the block:
m * a = m * g - M * g
Dividing both sides by m, we get:
a = g - (M * g) / m
Simplifying further:
a = g * (1 - M / m)
Thus, the acceleration of the block is g * (1 - M / m).