Question

A half Atwood machine is set up. The pulley is a solid disc of mass .5kg and radius 5cm. The system is released from rest with the 5kg mass 1 meter above the floor. (note, the mass that is connected to the 5.0 kg mass weighs 12.0 kg).

Answer the following two questions:

1. Determine the speed of the 5 g mass when it hits the floor.

2. Determine the speed with which the 5 kg mass will hit the floor or if the pulley is replaced by a massless one.

Thank you! there was a diagram for this question, however it wouldn' t load in

Answer 1

1.

m = 5 kg

M = 12 kg

m' = mass of disc = 0.5 kg

r = radius of disc = 5 cm = 0.05 m

using conservation of energy

Initial potential energy = final potential energy + kinetic energy + rotational kinetic energy

(m + M) g h = m g (2h) + (0.5) (m + M) v² + (0.5) I w²

(m + M) g h = m g (2h) + (0.5) (m + M) v² + (0.5) (0.5) (m' r²) (v/r)²

(m + M) g h = m g (2h) + (0.5) (m + M) v² + (0.25) m' v²

(M - m) g h = (0.5) (m + M) v² + (0.25) m' v²

(12 - 5) (9.8) (1) = (0.5) (12 + 5) v² + (0.25) (0.5) v²

v = 2.82 m/s

2)

replacing by pulley

using conservation of energy

Initial potential energy = final potential energy + kinetic energy + rotational kinetic energy

(m + M) g h = m g (2h) + (0.5) (m + M) v²

(m + M) g h = m g (2h) + (0.5) (m + M) v²

(m + M) g h = m g (2h) + (0.5) (m + M) v²

(M - m) g h = (0.5) (m + M) v²

(12 - 5) (9.8) (1) = (0.5) (12 + 5) v²

v = 2.84 m/s