Herriman High AP Physics C

Chapter 7

Work and Energy

Section 7.2What is Energy?

Energy deals with the state of an object.

We assign an energy value to a system of objects.

Energy in a System is always conserved.

No exception to this principle has ever been found.

Herriman High AP Physics C

Herriman High AP Physics C

Section 7.2Energy Conservation

All energy in a system is constant

Work and energy are interchangeable.

Doing work on a system either changes its kinetic energy and/or stores energy as potential energy.

Herriman High AP Physics C

Section 7.3Kinetic Energy

Kinetic Energy is energy of MotionAny moving object has kinetic energy

Dependent on the mass of the object and its velocity.

Mathematically expressed as:Ek = ½ mv2

Herriman High AP Physics C

Sample Problem

What is the kinetic energy of a car with a mass of 2000 kg moving at 30 m/s?

Ek = ½ mv2 = (½)(2000 kg)(30 m/s)2

= 900,000 Joules

Herriman High AP Physics C

Section 7.4Work

The Physics definition of work requires a displacement, i.e. an object must be moved in order for work to be done!

The Applied force which causes the displacement contributes to the work, i.e. in order to contribute to the work, the applied force must be parallel to the displacement.

Herriman High AP Physics C

Work: A Mathematical Definition

Work = (Force)(Displacement) W = F•s Work is the scalar product of two vectors.

Units of Work = (Newton)(Meter)1 Newton•Meter = 1 JouleA Joule is a unit of Energy and it takes energy to do work and work done on an object either causes it to move (kinetic energy) or is stored (potential energy)

Herriman High AP Physics C

Sample Problem

What work is done sliding a 200 Newton box across the room if the frictional force is 160 Newtons and the room is 5 meters wide?

W = Ff • ΔX = (160 N)(5 m)

800 Joules

Herriman High AP Physics C

Sample Problem

400 N

600 N

A box is pulled 30 M across a floor by a rope which makes a 30° angle with the horizontal. If the force exerted on the rope is 400 N, how much work is done?

Only Force in the direction of the motion does work. Hence,

W = F cos θ•s

= 400 cos 30° • 30 M

= 10320 Joules.

Section 7.5 Work and Kinetic Energy

Work done on an object changes its energy.

A change in kinetic energy can be set equal to the work done on the system.

½ mvf2 – ½ mvi

2 = Fxd

Herriman High AP Physics C

Herriman High AP Physics C

Section 7.6:Gravitational Potential Energy

Occurs due to the accelerating force of gravity

Is determined by the position of the object in the gravitational field

Mathematically determined by: Ep = mgh where m is mass, g is the acceleration due to gravity and h is the height above a determined baseline.

Herriman High AP Physics C

Sample Problem

What is the potential energy of a 10 kg rock sitting on a cliff 30 meters high? The acceleration due to gravity is 9.8 m/s2.

Ep = mgh = (10 kg)(9.8 m/s2)(30 m)

2940 Joules

Herriman High AP Physics C

Section 7.7: Work Done by Variable Forces

If the force applied in a problem varies with respect to position, then calculating the work done by that force requires integration. Hence

i

f

x

x

dxxFW )(

Herriman High AP Physics C

Section 7.7:A particle on a spring

Top picture is “rest position”; x = 0 No work is done

Bottom picture is “stretched position” Work has been done stretching the springFs = -kx

Herriman High AP Physics C

Section 7.7Particle on a Spring

Combining this with the previous equation:

W =∫F(x)dx and F = -kxWe get:

∫(-kx)dx = ½ kxi2 – ½ kxf

2

Herriman High AP Physics C

Sample Problem A wooden block with a mass of 6.4 kg

is hung vertically from a spring. This causes the spring to stretch 0.124 meters from its equilibrium position. What work is done by the block on the spring?

Summing the forces in the problem:∑F = mg-kx = 0; so kx = mg or k = mg/x and W = ½ kx2 so W = ½ mgx = ½ (6.4 kg)(9.8 m/s2)(0.124 m) = 3.89 J

Herriman High AP Physics C

Section 7.9: PowerPower = Work/time = Joules/Second

Mathematically there are two formulas for Power:

tdF

P or since FVP v

td

then

Herriman High AP Physics C

Sample Problem

What power is developed by a 55 kg person who does 20 chin ups, h = 3 m, in 45 seconds?

P= w/t = FΔd/t = mgh/t (20(55 kg)(9.8 m/s2)(3 m))/45 sec

= 718.6 Watts

Herriman High AP Physics C

Problem Types

WorkWork at an angleKinetic EnergyGravitational PotentialElastic PotentialConservationPower