Question

In an Atwood's machine, one block has a mass of 346.0 g, and the other a mass of 526.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 4.50 cm. When released from rest, the heavier block is observed to fall 64.2 cm in 2.29 s (without the string slipping on the pulley). What is the magnitude of the acceleration of the 346.0-g block? What is the magnitude of the acceleration of the 526.0-g block? What is the magnitude of the tension in the part of the cord that supports the 346.0-g block? What is the magnitude of the tension in the part of the cord that supports the 526.0-g block? What is the magnitude of the angular acceleration of the pulley? What is the rotational inertia of the pulley? What is the change in the potential energy of the system after 2.29 s?

Answer 1

1. d = v0 t + a t^2 / 2

0.642 = 0 + a(2.29^2)/2

a = 0.245 m/s^2 .....Ans

2. a = 0.245 m/s^2 (from string constraint)

3. F_net = m a

T1 - m1 g = m1 a

T1 = 0.346(9.8 + 0.245) = 3.48 N

4. F_net = m2 g - T2 = m2 a

T2 = (0.526)(9.8 - 0245) = 5.03 N

5. alpha = a / R = 0.245/0.045

alpha = 5.44 rad/s^2

6. Net torque = I alpha

r (T2 - T1) = I alpha

(0.045)(5.03 - 3.48) = I(5.44)

I = 0.0128 kg m^2

7. change in PE = (0.346 x 9.8 x 0.642) - (.526 x 9.8 x 0.642)

= - 1.13 J