**
Atwood's machine**

An early arrangement for measuring
the acceleration of gravity, called Atwood's Machine, is shown in the figure.
The pulley P and cord C have negligible mass and friction. The system is
balanced with equal masses M on each side as shown (solid line), and then a
small rider m is added to one side. The combined masses accelerate through a
certain distance h, the rider is caught on a ring and the two equal masses then
move on with constant speed, v. Find the value of *g* that corresponds to
the measured values of m, M, h, and v.

__Solution by __**Rudy Arthur & Nishit**

Calling the acceleration of the masses a and the tension on the cord T, Newton's 2nd law dictates that on the left side of the pulley,

(M+m)*g* - T = (M+m)a,

while on the right side,

T - M*g* = Ma.

Eliminating T gives,

a = m*g* / (2M+m).

Kinematically,

v^{2} = 2ah = 2 (m*g*/(2M+m)) h,

or rearranging,

*g* = (2M+m)v^{2} / 2mh.