P2aL9 How Much Energy?

Key Words

Air resistance - drag experienced by moving through air.

Distance - length between two points.

Elastic Potential Energy - energy contained in a stretch or squashed spring.

Energy - ability to do a job of work.

Force - push, pull or twist.

Friction - force opposing movement caused by surfaces rubbing against each other.

Gravity - a pull on objects attracting the to the Earth.

Kinetic energy - energy in a moving object.

Mass - the amount of material in an object.

Potential energy - energy stored in a raised object that can do work when it falls.

Stopping distance - the total distance from when a driver sees an emergency to the car coming to a stop.

Transformed - energy converted from one form to another.

Transferred - energy has been moved.

Weight - the force due to gravity on a mass.

Work done - energy expended to do a job.

Grade E

Kinetic energy increases when:

• the mass increases.

• the speed increases.

When a fast moving car hits a stationary object energy is transferred.  This results in the bodywork of the car being crushed; work is done to do this.  Energy and work are very closely related:

Work done (J) = energy transferred (J)

If you lift a weight against gravity, you are doing a job of work.  The energy is being transferred to potential energy.  If you drop the weight, the potential energy will be turned into kinetic energy, which you will fell as it hits your foot (an brings tears to your eyes).

Grade C

Work done is also linked to the force applied:

Work done (J) = force (N) × distance moved in the direction of the force (m)

In Physics Code:

W = Fd

In triangle form:

The distance in the direction of the force is important.  

Elastic potential energy is the energy stored in a rubber band or stretched spring.  If we fire a ball into the air with a rubber band, we will transfer the elastic potential energy into gravitational potential energy.  The experiment below is called the bungee jump:

The potential energy is worked out using this equation:

Potential energy (J) = mass (kg) × acceleration due to gravity (m/s²) × vertical height (m)

In Physics code:

E_p = mgh

This will not give us a totally reliable result for the elastic potential energy, as some is lost as heat.  But it will be a reasonable estimate.

Grade A

Kinetic energy is given by the equation:

kinetic energy (J) = 1/2 × mass (kg) × (speed (m/s))²

In Physics Code:

Suppose we use a force F to accelerate an object steadily from zero up to a speed v.  The kinetic energy is the same as the work done.

Kinetic energy (J) = force (N) × distance moved (m) .......Eq 1

Since:

Force (N) = mass (kg) × acceleration (m/s²)

we can write:

Force (N) = mass (kg) × [change in speed (m/s) ÷ time (s)]

In Physics code:

F = m × [(v - 0) ÷ t] = m × v/t

Now:

distance travelled = average speed × time

In Physics code:

d = [(v - 0) ÷ 2] × t = 1/2 v × t  .........Eq 2

Combining equations 1 and 2:

Kinetic energy = F × d

Ek = m × v/t × 1/2 v × t

The t terms cancel out to give us:

Ek = 1/2 mv²  [Boom! Boom!]

The ability to follow this derivation is the sort of thing that will distinguish the outstanding student (A*) from the excellent student (A).

Note that we have talked about speed rather than velocity.  The kinetic energy of an object is the same regardless of direction.  We can say this, because of we have a negative velocity, the kinetic energy will still be positive, since minus times a minus is a plus.