Question

Atwood machine :
Atwood used the system to prove Newton's laws of motion. Atwood machine consists of two loads of masses m, and m, attached to the ends of a limp of inextensible string as shown in the adjacent figure. The string runs over a pulley. Find the acceleration of each load and tension in the string (m, > m.)​

Answer 1

We know that tension of string always tries to pull the bodies up.

Explanation:

There exist two forces on the load of mass m1, one is tension of the string acting in upward direction and weight of the load (m1g) acting in downward direction.

The net force on m1Fnet=m1a

⇒m1g−T=m1a−−−−−−−−−−−−−−−(1)

Thus the net force (Fnet) acting on mass m1 produces an acceleration .a. in it.

When m1 moves down, m2 moves up. So the magnitudes of acceleration are same.

From the FBD of mass m2

Fnet=T−m2g=m2a−−−−−−−−−−−−−−−−(2)

Solving (1) and (2) equations, we get

a=(m1−m2g)/m1+m2

T=2m1m2/gm1+m2