Chapter 5: Work & EnergyThe Work/Energy Relationship

• Work is the use of force to displace an object in the direction of the force.

• If an object is not displaced when a force is applied to it, then no work has been done on that object.

Work done by a constant net force:W = Fx∆x

For forces applied at an angle, θ: W=Fcosθ d

“d” is the magnitude of displacement

Work is only done when a force causes an object to move some distance.

Work is measured in units called Joules (J).

Work is a scalar quantity that can be positive or negative.

• Positive work results in a displacement in the same direction as the applied force.

• Work is negative when the force is opposite the displacement.

Fnet

Displacement

Fnet

Displacement

Friction is doing negative work on the box.

Fk

• Frictional work is done whenever the force of friction hinders motion. For instance, when pulling a sled over concrete, a

significant amount of friction prevents the sled from being pulled as far.

Work done by friction:Wf = FkΔx

• Applying force at an angle can alter the frictional force.

Reduction of frictional force because Fy is upward, and reduces

the normal force.

Increase of frictional force because Fy is downward, and increases the

normal force.

Fy

Fy

• The net work done on an object can be expressed as the change of the object’s kinetic energy.

• This expression is known as the “Work - Kinetic Energy Theorem.”

• Kinetic Energy is the energy of an object due to its motion.

Net Work Done on an Object:Wnet = ∆KE = ½mv2 – ½mv0

2

Kinetic Energy of an Object:KE = ½mv2

• Friction is an example of a nonconservative force – one that randomly disperses the energy of the objects on which it acts.

• For example, the car shown is undergoing frictional forces as it slides.

• The energy is being dissipated as sound waves and thermal energy.

• Gravity is an example of a conservative force. It does not dissipate energy.

• In order to reach the top of the cliff, the man had to use energy to work against gravity.

• This energy used as work is recovered as KE by diving.

• Upon reaching the water, his speed gives him kinetic energy equal to the work he used to climb upward.

• In general, a force is conservative if the work it does moving an object between two points is the same regardless of the path taken.

Conservative forces can recover the work they do as potential energy.

• Potential energy is the stored energy that results from an object’s position or condition.

It depends only on the beginning and ending points of motion…not the path taken.

• Gravitational PE is the product of an objects mass, gravitational acceleration, and height.

• The work done by gravity is the negative of the change in gravitational potential energy.

Gravitational Potential Energy:PE = mgy

*Can also be expressed as “weight x height”

Work done by gravity:Wg = -( PEf – PEi ) = -( mgyf – mgyi )

• Suppose that friction (or some other nonconnservative force) does work on a mechanical system:

• For example – a firefighter sliding down a pole to reach the first floor.

Work done by a nonconservative force:Wnc = ΔKE + Δ PE

• The Law of Conservation of Energy states:ENERGY CAN NEVER BE CREATED OR DESTROYED.

• Applying this to KE and PE, we develop the Law of Conservation of Mechanical Energy: The total mechanical energy of an isolated

system will remain constant.

Conservation of Mechanical Energy:KEi + PEi = KEf + PEf

If gravity is the only force doing work:½mv2

i + mgyi = ½mv2f + mgyf