Question

A block of mass 8 m can move without friction

on a horizontal table. This block is attached
to another block of mass 34 m by a cord that
passes over a frictionless pulley.


If the masses of the cord and the pulley
are negligible, what is the magnitude of the
acceleration of the descending block?

Answer 1

The magnitude of the acceleration of the descending block is g/10, where g is the acceleration due to gravity.

Step-by-step explanation:

The acceleration of the descending block can be determined using Newton's second law of motion. Since the masses of the cord and the pulley are negligible, the only force acting on the system is the force of gravity. The 8m block on the table experiences a downward force of 8mg, while the 34m block hanging vertically experiences an upward force of 34mg. The net force on the system is the difference between these forces, which is (34m - 8m)g = 26mg. According to Newton's second law, F = ma, where F is the net force and m is the total mass of the system. Therefore, the acceleration can be calculated as a = F/m = (26mg)/(8m + 34m) = g/10.

The magnitude of the acceleration of the descending block is therefore g/10, where g is the acceleration due to gravity (approximately 9.8 m/s²).

Answer 2

Let M1 = 8 kg and M2 = 34 kg

F = M a = (M1 + M2) a

F = M2 g the net force accelerating the system

M2 g = (M1 + M2) a

a = M2 / (M1 + M2) g = 34 / (42) g = .81 g = 7.9 m/s^2