Energy, Work and Power Study Guide
Energy – (unit: joule) Measure of the capacity to do work. Forms of energy: kinetic, potential,
mechanical, chemical, electric, magnetic, radiant, nuclear, gravitational, thermal, heat, etc..
Kinetic Energy Formula: Ek = ½ m v2
Potential Energy Formula: Ep = m g h
Law of conservation of energy – The total energy of an isolated system is constant. Energy can be
transferred/converted from one form to another but energy
cannot be created or destroyed. (also known as the first law of
thermodynamics)
Work – (unit: joule) Occurs when an object is displaced (moved) due to a force.
Work Formula: W = F d
or
work (J) = force (N) x distance (m)
Joule (J) - Unit of energy and work. One joule is defined as being equal to the force of one Newton on
an object moved a distance of one meter. One joule of electrical energy is equal to one
amp flowing through a one Ohm conductor for one second.
Power – (unit: Watt) The rate at which work is done. 1 Watt = 1 Joule of work/second
1 Watt is also equal to the electrical power of 1 amp at 1 volt.
Power Formula: P = J/s
or
power (W) =
joules (J)
seconds (s)
Efficiency – A measure of how well a device’s input energy is converted to useful output energy. For
example, if we input 100 joules of energy into a machine that lifts an object and has an
output energy of 100 joules, the machine is 100% efficient. There is no machine that is
100% efficient because energy will be lost/transferred to something other than the
intended purpose of the machine.
Efficiency Formula:
Efficiency =
useful energy(work output)
total energy(work input)
x 100
Force – (unit: Newton) Causes a change in an object’s motion. In other words, a force will cause an
object to accelerate (change velocity). One Newton (N) is equal to the amount of force
required to accelerate a 1 kg mass at 1 m/s2.
Math Problem Examples (formulas and solved equations)
1) How much power is used by a light bulb that uses 2000 joules in 40 seconds?
2000 𝐽
Formula: J/s = Watts
40 𝑠
= 50 Watts of power
2) How much power does a pulley system provide if 5000 joules of energy are applied for 10
seconds? (assume 100% efficiency)
5000 𝐽
Formula: J/s = Watts
10 𝑠
= 500 Watts of power
3) How many seconds did a light bulb stay lit if it uses 3000 J of energy and has a power output
of 100 watts? (assume 100% efficiency)
3000 J
Formula: J/s = Watts
30 s
= 100 Watts of power
4) What is the efficiency of a light bulb in which you input 150 joules of electrical energy and get
out 30 joules of light?
Formula:
useful energ output
total energy output
x 100 = efficiency
30 𝐽
150 𝐽
x 100 = 20% efficiency
5) How much work has been done if a dude pushes with all his might on a wall with 150 N of
force and is not able to move the wall?
Formula: Fd = work
(150 N ) x
(0 m) = 0 joules of work
6) How much force is required to lift a box that requires 400 J of work to lift the box 2 m?
Formula: Fd = work
(200 N) x (2 m)
= 400 Joules of work
7) What is the kinetic energy of a ball that has a velocity of 30 m/s and a mass of 2 kg?
Formula: Ek = ½ m v2
½
x (2 kg) x (30 m/s)2 = 900 joules of kinetic energy
8) What is the mass of a ball that has a kinetic energy of 250 J and a velocity of 50 m/s?
Formula: Ek = ½ m v2
½
x (0.72 Kg) x (50 m/s)2
= 250 Joules of kinetic energy
9) What is the velocity of a ball that has a kinetic energy of 500 J and a mass of 5 kg?
Formula: Ek = ½ m v2
½
x (5 kg) x (14 m/s)2 = 500 Joules of kinetic energy
10) What is the potential energy of a 5 kg ball that sits on a roof of a 20 m tall building?
Formula: Ep = m g h
(5 kg) x (10 m/s2) x (20 m) = 1000 joules of potential energy
11) What is the height of a ball that has a potential energy of 5000 J and a mass of 2 kg?
Formula: Ep = m g h
(2 kg) x (10 m/s2) x (250 m) = 5000 joules of potential energy