Question

In the Atwood machine shown in (Figure 1) , the pulley radius is 0.10 m , and the rotational inertia of the pulley is 0.17 kg?m2 . Ignore the cord's inertia.

A)Calculate the acceleration of the blocks.

B)Calculate the tension in the cord on the left

C)Calculate the tension in the cord on the right.

Answer 1

a) for 5 kg ( Fnet = ma)

5g - T1 = 5a ......(i)

for 2kg :

T2 - 2g = 2a ......(ii)

for pulley (torque = I x alpha)

r(T1 - T2) = I ( a/r)

T1 - T2 = (I/r^2)a = (0.17 / 0.1^2) a

T1 - T2 = 17a .......(iii)

(i) + (ii) + (iii) =>

5g - 2g = (5 + 2 + 17)a

a = 1.225 m/s^2

B) 5g - T1 = 5a

T1 = 5 ( g- a) = 5 (9.8 - 1.225)

T1 =42.875 N

C) T2 - 2g = 2a

T2 = 2( g + a) =2 ( 9.8 + 1.225)

T2 = 22.05 N