EXAMPLE QUESTIONS:

CONSERVATION OF ENERGY

• Explain what is meant by "conservation of energy"

• Calculate the kinetic energy of a moving object or collection of objects (slow compared to the speed of light) 

33) Two balls with mass 1kg appraoch each other, each with speed 10 m/s. Calculate the total momentum and total kinetic energy of the balls.

• Calculate the potential energy of an object in a uniform gravitational field, or of a stretched or compressed spring (solid)

34) Two springs with normal length 10cm are stretched to 14cm and compressed to 8cm. Relative to the first, how much potential energy does the second have?

• Describe the relation between thermal energy and kinetic energy

• Compare the potential energy of two configurations to decide which is higher

35) The potential energy of a proton and an electron is larger when they are A) closer together B) further apart

• Explain why Hooke's law should hold quite generally for slightly stretched or compressed solids or other static systems that are displaced from their equilibrium configurations

• To decide whether mechanical energy is conserved in specific scenarios

36) For which of the following situations is mechanical energy conserved?

A) A block sliding along a table with friction
B) Two balls in an inelastic collision
C) A ball sliding down a frictionless ramp.
D) An object falling at terminal velocity

• To use conservation of mechanical energy to determine final velocities or configurations in situations where it applies

see  October 7th worksheet for examples

• To use conservation of energy together with conservation of momentum to determine final velocities of objects in elastic collisions in terms of their initial velocities.

see October 7th worksheet and Mastering Physics problems for examples

WORK, ENERGY, AND POTENTIALS

Students should be able to:

• Describe qualitiatively the types of energy transfer occurring in various physical processes

 Describe the types of energy transfers involved in the following processes:

-A block sliding down a ramp with friction.
-A person riding a bicycle
-A rocket flying up to space

• Calculate the energy expended in a certain process given the applied force at each location (whether the force is parallel to the displacement or in a different direction).

We push a 10kg block 10 meters along a table with coeffeicient of friction 0.2. How much work have we done on the block?

A 100kg block slides down a 20 meter long 45 degree ramp with coefficient of friction 0.1. How much work does friction do on the block? Using your result and conservation of energy, determine the final speed of the block if its speed was zero at the top of the block.

• Identify the equilibrium position of an object given its potential energy as a function of position

• Calculate the force on an object due to a spatially varying potential energy

An non-Hookian spring is manufactured so that the potential energy stored in the spring is U(X)  = 3J (X / 1cm)  + 4J (2cm / X), where X is the length of the spring. If we attach one end of the spring to a wall and attach a mass to the spring (on a horizontal frictionless table), what is the equailibrium position of the mass? What is the force on the mass if we move it to X=5cm? What is the force on the mass if we move it to X=1cm? Sketch the force on the mass as a function of X.

If we instead attached the same spring to the ceiling, what would be the equilibrium position of mass? If we pull down the mass so that the spring has length  10cm, the mass will accelerate upwards. How high will it get before it starts coming down? At what height will its speed be maximum? If the mass is 50g, what is this maximum speed?