Work, Energy and Power

Is the student doing work in pushing against the wall?

Is the girl doing work in pushing the cart?

Is the man doing work in carrying the load across the street?

Is the lady doing work while holding the weights above her head?

Is work done in lifting the box?

Is work done in putting down the box?

Work If a constant force F acts on an object as it

undergoes a displacement d, the work done by the force on the object during the displacement is

W = Fdcos

where W = work done in Joules (J)

F = force in N

d = displacement in m

= angle (180 or less) between the

direction of F and the direction of

d

Note: 1 J = 1 Nm

Work

Requirements in order for work to be done

1. Force need to be exerted

2. There must be a displacement

3. The force must be exerted in such a way that it has a component that is in the same direction or opposite to the direction of the displacement.

Energy

The capacity of a physical system to do work.

Kinetic Energy (KE)The energy an object has because of

its motion.

where KE = kinetic energy in J

m = mass in kg

v = speed in m/sThe kinetic energy of an object

changes when its speed changes from vi to vf.

Gravitational Potential Energy (PEg)

The energy an object has because of its vertical separation from the Earth’s surface.

where PEg = gravitational potential

energy in J

m = mass in kg

g = acceleration due to gravity (9.8 m/s)

h = height of the location of the object in m The gravitational potential energy changes when the

vertical location of the mass changes from hi to hf

Elastic Potential Energy (PEs)

The energy of an object such as a spring has because it is compressed or stretched from its equilibrium position.

where PEs = potential energy in J

k = force constant in N/m

x = displacement of the spring in m The elastic potential energy of a spring

changes when its displacement changes from xi to xf.

Work-Energy Calculation

When a system gains or loses energy from its environment because of work done on the system by forces origination in the environment, then the change in the system’s energy is

W = Ef – Ei

Rearranging and substituting for the different types of energy results to

KEi + PEgi + PEsi + W = KEf + PEgf + PEsf

Law of conservation of energy

In a closed, isolated system, energy is not created or destroyed, but rather, is conserved.

KEi + PEgi + PEsi = KEf + PEgf + Pesf

Power

The rate of doing work or the rate of energy conversion from one form to another.

where P = power in Watts (W)

W = work done in J

E = energy in J

t = time in s