Question 5

A 12 kg weather rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550 N/m, is anchored to the ground. Initially, before the engine is ignited, the rocket sits at rest on top of the spring. The spring is compressed by 20 cm.

After the engine is ignited, what is the rocket’s speed when the spring has stretched 40 cm?

Assume no air drag.

Question 4

A 1500 kg car travelling at 10 m/s suddenly runs out of gas while approaching the valley shown in the figure above. The alert driver immediately puts the car in neutral so that it will roll. What will be the car's speed as it coasts into the gas station on the other side of the valley? 

Assume there is no friction of any kind.

Question 3

A horizontal spring with spring constant 100 N/m is compressed 20 cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. 

Use conservation of energy to calculate how far the box slides across the rough surface before stopping.

Question 2 (cont.)

c) Suppose the particle's energy is lowered to 4.0 J. Can the particle ever be at x = 4.0 m?

Question 2 (cont.)

b) What is the particle's speed when it is at x = 4 m?

Question 2

The figure above shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J.

a) Where are the particle's turning point/s? 

Question 1

The potential energy function of a particle is given by 

U(x) = - (x - 3)²

a) Calculate the corresponding conservative force. 

Question 1 (cont.)

b) Calculate the equilibrium point, and state whether it is stable or unstable.

Question 4 (cont.)

(b)   

Calculate the work done by kinetic

friction. The coefficient of kinetic friction

Question 5

A particle

is attached to a horizontal spring as it moves from x = -0.1 m to x = 0.1 m

along the x-axis. The spring constant is 2.0 N/m.

Calculate

the work done by the spring force on the particle from the initial to the final

position.