11Cexamples2


 * Connected Weights and Pulleys**

**Example 1**

Two masses (2 kg and 4kg) are connected by a light inelastic string. The first mass is being pulled by a 10 Newton force across a __smooth__ horizontal table. Find the acceleration of the two masses and the tension in the string. To find acceleration, the only horizontal force is the pulling force of 10 Newtons, so we can treat the two masses as one unit. {If friction was involved then we would need to analyse the two masses seperately but they would both have the same acceleration.}


 * R = ma
 * 10 = (2 +4)a
 * ** a = 1.67 m/s 2 **

The only horizontal force acting on the second mass is the Tension, and we know the second mass has an acceleration of a = 1.67, so


 * R = ma
 * T = 4 x 1.67
 * ** T = 6.67 Newtons **

A mass of 1.5kg is connected to a mass of 3kg by a light inelastic string that passes over a smooth pulley and allows the two masses to hang freely. Find the acceleration of the system and the tension in the string.
 * Example 2 [[image:bhs-specialist/11Cdyn5.gif width="224" height="247" align="right"]]**

For the 1.5 kg mass ... ... {The mass is travelling up}
 * R = ma
 * T – 1.5g = 1.5a
 * T = 1.5a + 1.5g ..... ** (1) **

For the 3kg mass ... ... { The mass is travelling down}


 * R = ma
 * 3g – T = 3a
 * T = 3g – 3a ..... ** (2) **

Combine the two equations ** (1) ** = ** (2) **


 * 1.5a + 1.5g = 3g – 3a
 * 4.5a = 1.5g
 * a = 0.33g
 * ** a = 3.27 m/s 2 **

Now find T, use ** (1) **:

.
 * T = 1.5a + 1.5g
 * T = 1.5 x 3.27 + 1.5g
 * ** T = 19.60 Newtons **