Atwood machine ---

Question

A 5.00 kg object placed on a frictionless, horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 8.50 kg object, as shown in the figure. Find the magnitude of the acceleration of the two objects and the tension in the string.

(a) acceleration of 5.00 kg object in m/s²

(b) acceleration of 8.50 kg object in m/s²

(c) tension in the string in N

Answer 1

So, the 5kg mass is being accelerated by the tension in the cord. The 8.5 kg mass is being accelerated by it's weight minus the tension in the cord. If we take g = 10m/s², we get the following two equations (using Netwon 2 which says that Net force = ma)

t = 5a.......(1)

85 - t = 8.5a........(2)

Subbing eqn 1 into eqn 2 we get 85 - 5a = 8.5a, so 13.5a = 85, so a = 6.30 m/s²

a) 5kg accelerates at 6.30 m/s² to the right

b) 8.5 kg accelerates at 6.30 m/s² downwards

c) t = 5 x 6.30 = 31.5 N