Question 1.2

A crate of mass, m₁, sits on a rough surface and is connected by a rope over a pulley to a

second mass, m₂, hanging over a cliff. The surface has coefficient of friction, μ. The two

masses are initially held at rest. Rope mass, pulley mass and pulley friction can be neglected.

a) Draw free body diagrams for the elements of the system.

[6 marks]

b) What is the acceleration that occurs when the masses are allowed to move?

[10 marks]

c) What is the velocity after m₂ has fallen by a distance, h? Assume that m, remains on

the surface and does not reach the cliff.

[4 marks]

m₂

M₂

m₁ = 15 kg

m₂ = 10 kg

μ = 0.4

h = 5m

Total for Question 2: 20 marks/nQuestion 1.1

A prototype of the novel satellite launching system, 'SpinLaunch', was recently tested. The

system uses angular acceleration to spin a satellite-carrying projectile up to a supersonic

speed and then releases it, tangentially and upward, into the atmosphere.

Vt

Support

arm

Projectile

V₁ = 450 m/s

r = 16.5 m

Assume that the moment of inertia, I, of the support arm and the applied torque, T, are

both constant. Also assume that T = 30 000 Nm.

a) Compute the angular velocity, w, required for the launch velocity, vt. [4 marks]

b) Determine the centripetal acceleration of the projectile just before it is released.

[3 marks]

c) Compute the angular acceleration used to spin the support arm and projectile, given

that the time required to move from rest to launch velocity is, T = 700 s. [4 marks]

What is the work done to move the projectile from rest to the launch velocity?

d)

[6 marks]

[3 marks]]

Total for Question 1: 20 marks

e) What is the power output of the system just before launch?