Work and Energy

Work…

…is the product of the magnitude of displacement times the component of force parallel to the displacement.

W = F‖ dUnits: N·m or Joules (J)

Work = Fd cos

Consider a crate pulled across a surface. Where… F is the applied force d is the displacement θ is the angle between the force

and the direction

F

d

F‖ = Fcosθ

θ = ZERO in this situation!!! The force and the displacement are in the same directionF

d

Work = Fd cos

Consider the same crate being pulled up an incline…

Work

Net work in moving an object is independent of the path to get there.

More force neededShorter distance traveled

Less force neededGreater distance traveled

Same amount of work done

Energy – What is it?

The ability to do work

KineticGravitational PotentialElastic Potential

HeatLightSoundElectricalChemicalNuclear

Types of Energy

Mechanical Energy – energy associated with an object’s position or

motion

Consider a cart with an initial velocity vi and a net force acting on it through a distance d…

viFnet Fnet

vf

d

Wnet = Fnet d

Remember F = ma = m(vf2 – vi

2/2d)So…

Wnet = m(vf2 – vi

2/2d)d

Wnet = m(vf2 – vi

2/2)

Wnet = ½ mvf2 – ½ mvi

2

Energy - Kinetic

Kinetic Energy is the energy that an object possesses due to its motion

If the mass of a body is m and its speed is v then its kinetic energy is given by

KE = ½ mv2

Work-Energy Theorem

W = ½ mvf2 – ½ mvi

2

W = ΔKE

The net work done on an object (by a net force) is equal to a change in kinetic energy of the object

Example problem

-A 10.0 kg sled is initially moving across a frozen pond at a speed of 4.2 m/s. How far will it travel if the coefficient of friction between the sled and ice is 0.10?

Energy - Potential

• Potential Energy – the energy of an object due to its position, shape, or condition

• An system acquires potential energy when work is done against another force

Energy - PotentialGravitational Potential Energy

This is the energy of an object associated with its position in a gravitational field (work done against the force of gravity to put it there)

GPE = mgh m = mass of the object h = height of object above some fixed

position (the position is arbitrary) g = the acceleration due to gravity

Energy - Potential

Elastic Potential Energy This is the energy that an object possesses

due to its position of being stretched or deformed (work done against the elastic restoring force)

FOR A SPRING (or similar)…EPE= ½ k x2

x = amount of stretch k = the spring constant (a characteristic of

the object being stretched)

The Principle of Conservation of Energy

Energy can be transformed from one form to another, but it cannot be created nor destroyed, i.e. the total energy of a system is constant

Energy transformations occur when work is done

Conservation of Energy

Since energy is conserved for a system, when we compare the total at two different points…

Total E1 = Total E2

KE1 + GPE1 + EPE1 = KE2 + GPE2 + EPE2

Power

Power is the rate of doing work or the rate at which energy is transferred.

P = W/tUnits: J/s = Watt

Alternate: P = W/t = Fd/t = Fv