Download Physics 083 – Work, Power and Energy Work is done when a force

Physics 083 – Work, Power and Energy
Work is done when a force is exerted on an object to move it a certain distance. In
short,
W=Fd
Work = Force x distance
If you work out the units for this then:
W=Nm
= Joule (J)
The joule is named after physicist James Prescott Joule and is define so that 1 Joule
of work is done when a 1 N force moves an object 1 metre. Work is only done if the
object is actually moved.
Work is also the area under an F vs. d graph. What is the work done in the graph
below?
The same is true with varying force. What is the work done in the graph below?
Example:
A 3 kg box is pulled by a rope with a 30 N force for 10m. The surface has a  = 0.2.
What is the acceleration of the box?
What work is done to overcome friction?
What work was done to move the box?
The same box is now pulled with the same 30 N force but it is exerted at a 30° angle.
How does the problem change? What is acceleration of the box this time?
Kinetic Energy
From kinematics we know:
vf2 = vi2 + 2 a d
or
vf2 – vi2 = 2 a d
but we also know that F = m a or a = F/m; therefore
vf2 – vi2 = 2 F d/m
if we multiply by m we get
m vf2 – m vi2 = 2 F d
then divide by 2 (or multiply by ½)
½ m vf2 – ½ m vi2 = F d
but W = F d and we can define Ek = ½ m v2
Ekf – Eki = W
This is the Work-Energy Theorem
 Ek = W
Work is equal to the change in kinetic energy of a
moving object
From a unit point of view
W=Fd
=Nm
W =  Ek = ½ m v2
= kg m2/s2
= (kg m/s2)(m)
= kg m2/s2
How much energy is there in a 2500 kg car traveling down the highway at 80
km/hr? How much work do the brakes need to do to stop it?
Potential Energy
Objects also have potential energy (Ep) because of their position. This is caused by
gravity.
Ep = m g h
Potential Energy = (mass)(acceleration due to gravity)(height)
The key to potential is to define the “zero” potential energy position.
How much potential energy is there in a 3.5 kg book that is 2.5 m off the floor? How
much kinetic energy will it have if it falls back to the floor? How much work will it
do when it hits the ground?
Power
Power is the rate at which work is done.
P=W/t
= J / s = watt (W)
A 3 kg box is moved with a 30 N force for 10 m.
1.
What is the work that is done?
2.
What power was needed to move it?
Law of Conservation of Energy
The Law of Conservation of Energy states that in a closed system, the total energy in
the system is conserved. It can however change from one form to another through
an energy transformation.
 Etotal = 0
Example:
A 5 kg rock is dropped from the edge of a 100 m cliff. How fast will the rock be
travelling just before it hits the ground below?
A 5 kg rock is thrown upward at 20 m/s from the edge of a 100 m cliff. How high
does it go? How fast will the rock be travelling just before it hits the ground below?
A 75 kg skier travels at 3.5 m/s at the top of a 6.5 m hill. At the bottom of the hill
they are travelling at 8 m/s. How much energy is lost as heat in going down the hill?
Another point. Although total energy is always conserved, kinetic energy may or
may not be conserved:
If  Ek = 0 (or Eki = Ekf) then we have an elastic collision.
If  Ek  0 (or Eki  Ekf) then we have an inelastic collision.
A 3 kg ball travels at 2 m/s E. It collides with a 2 kg ball at rest. If the 2 kg ball moves
E at 2 m/s, what is the velocity of the 2 kg ball? Is the collision elastic or inelastic?