Work, Energy Power

Textbook chapter 5

Work done

• Work done = force × distance moved in the direction of the force

• W=Fx

• Units: joules(J, =Nm)

Gravitational potential energy

• The capacity for doing work as a result of an objects position in a gravitational field

• Unit: joules(J, =Nm)

Equation for gravitational potential energy

E_p = mgh

Kinetic energy

• Energy associated with an object as a result of its motion

• Units: joules(J, =Nm)

• E_k α m

• E_k α v²

Equation for kinetic energy

E_k = ½ mv²

Power

• Rate of work done

• Unit: watts(W, =Js^-1)

Equation for power

• P=W/t

• P=E/t

Equation for power in terms of force and velocity

P=Fv

Efficiency

• Efficiency = (useful output energy) / (toatal output energy) × 100

Smooth surface

A surface with no friction.

The principle of conservation of energy

The total energy of a closed system remains constant - energy cannot be created nor destroyed

Deriving the equation for kinetic energy

v² = u² + 2as and F = ma and u = 0

v² = 2(F/m)s = 2 (Fs)/m = 2 E_k/m (since Fs = work done)

So E_k = ½ mv2

Deriving equation for gavitational potential energy

Work done = Force × distance = weight × height = (mg)h

So E_p = mgh

Deriving P=Fv

Power = Work done / time = (Force × distance) / time = Force × (distance / time) = Force × velocity

So P=Fv