Chapter 5 Work and Energy. Review x = v i t + ½ a t 2 x = ½ (v i + v f ) t v f = v i + a t v f 2 = v i 2 + 2a x.

Chapter 5

Work and Energy

Reviewx = vit + ½ a t2

x = ½ (vi + vf)t

vf = vi + at

vf2 = vi

2 + 2ax

F = ma

Kinetic friction is a resistive force exerted on a moving body by

its environment.

Section 5-1Work

WorkThe product of the

component of a force along the direction of displacement and the

displacement.

Work = Force x Displacement

Instead of using x, use ‘d’.

W = FdNote: It’s the Fnet doing the

work.

Work is done only when the

components of a force are parallel to the displacement.

No Movement, No Work

When the net force is at an angle to the direction

of the displacement.

W = Fd(cos

•If is 0, then cos 0 = 1; therefore, the equation is just W = Fd

)(cos dFW netnet

Units of WorkFrom the equation, we get Newton-meters (N-m).

Another name for a N-m is a Joule (J)

1 J = 1 N-m

Ex 1: Andy is out pulling his wagon again, if he pulls the wagon with a force of 60 N at an angle of 35 degrees to

the ground. How much work is done, if he pulls it

15 m?

G: F = 60 N, d = 15 m, =35o

U: W = ?

E: W = Fdcos

S: W =

S: W =

Ex 2: Greg applies a net force of 550 N, at an

angle of 33 degrees to the ground, to help move a car. If he does 2500 J of work, how far does he

move the car?

G: F =550 N, W=2500 J, =33o

U: d = ?

E: W = Fd(cosor d =W/(Fcos)

S: d =

S: d =

Work is a scalarIt’s (+) when the force is in the same direction as the displacement.

It’s (-) when the force is in the direction opposite of the displacement.

(+) Net Work1. Object speeds up

2. Work is done on the object.

(-) Net Work1. Object slows

down2. Work is done by

the object.

Section 5-2Energy

EnergyThe ability to do

work.

Kinetic Energy(K.E.)

Energy of an object due to its motion.

K.E. depends upon speed and mass.

½ mv2 is called ‘Kinetic Energy’

K.E. = ½ mv2

(A)

G: mshot=7 kg, vshot=3m/s

U: K.E.shot = ?

E: K.E. shot=½ m shot v shot2

S: K.E. shot =

S: K.E. shot =

(B)G: K.E.bb = 31.5 J, m =1.5 kg

U: v bb = ?

(B)G: K.E.bb = 31.5 J, m =1.5 kg

U: v bb = ?

E:bb

bb m

EKv

..2

S:bbv

S:

S: v bb =

bbv

Work–Kinetic Energy Theorem

The net work done on an object is equal to the change in the kinetic Energy of the object.

Net Work = change in K.E.

Wnet= K.E. = K.E. f - K.E. i

Fnetdcos ½mvf2 - ½mvi

2

Fnetdcos Wnet= K.E. = K.E. f - K.E. i = ½mvf2 - ½mvi

2

They are all equal to each other.

..EKWnet

Ex 4: On a frozen pond, Joe kicks a 10 kg sled, giving it an initial speed of 2.2

m/s. How far does the sled move if the coefficient of friction between the ice

and the sled is 0.10?

G: m = 10kg, vi = 2.2 m/s, vf = 0 m/s, k =0.10

U: d = ?

E: Wnet = K.E.

Fnetdcos= ½mvf2 - ½mvi

2

The net force is only due to friction, so Fnet = kmg. Because it is slowing down.

kmgdcos= - ½mvi2

The force acts in the opposite direction of motion, so = 180.

d = (- ½mvi2)/

(kmgcos

S: d =S: d =

Potential Energy (P.E.)

Energy associated with an object due to the position of

the object.

•Examples: Wound clock spring, compressed spring, or an object above the floor or ground.

Gravitational Potential Energy (P.E.g)

The P.E. associated with an object due to the position of the object relative to the Earth or some other gravitational source.

Potential Energy Equation Derivation

We know energy is work

P.E. = W

P.E. = Fd

• The force acting on the body is its weight and the distance it

falls is the height.

P.E.g = Fgh

P.E.g = mghThis is called Gravitational

P.E.

Work is done only when a body is

allowed to move or fall from a higher

level to a lower level.

• Both blocks acquire the same gravitational potential energy, mgh.

• Both blocks acquire the same gravitational potential energy, mgh.

• The same work is done on each block.  What matters is the final elevation, not the path followed.

Difference between the P.E. of a body at a higher level and a lower level is the energy released to

do work.

Zero LevelIs the selected level an

object is allowed to fall to, usually the

floor or the ground.

EX 5: What is the P.E. of an Elevator having a mass of

500 kg, when its 25 m off the ground?

G: m = 500 kg, g = 10 m/s2, h = 25m

U: P.E.g = ?

E: P.E.g = mgh

S: P.E.g =

S: P.E.g =

Ex 6: A student weighing 500 N walks up a flight of stairs to a height 3.5 m higher than started from. How much P. E. did he gain?

G:Fg=mg=500 N, h=3.5 m

U: P.E.g = ?

E: P.E.g = mgh

S: P.E.g =

S: P.E.g =

Elastic Potential Energy(P.E.elastic)

The P.E. in a stretched or compressed elastic

object.

When a force compresses or stretches a spring, elastic P.E. is stored in the spring.

P.E.elastic = ½ kx2

Where:

k = spring constant (N/m)

x = distance compressed or stretched

•The length of a spring with no external force on it is called the relaxed length.

The amount of P.E. stored depends upon how far the

spring is stretched or compressed.

Section 5-3Conservation of

Energy

Mechanical Energy- Energy associated with the motion/positon of an object.

- The sum of K. E. and all forms of P. E.

M.E. = K.E. + P.E.

In the absence of friction, the total M.E. remains the same at any point.

This is called the Conservation of

Mechanical Energy

Energy can not be created nor

destroyed, it can just change its form

of energy.

Although the amount of M.E. is constant, the form of energy can

change.M.E. i = M.E.f

K.E.i + P.E.i = K.E.f + P.E.f

½ mv2i + mgh i

= ½ mv2

f + mghf

Ex 8: Starting from rest, Ashley zooms down a frictionless slide from an initial height of 3.0 m. What is her speed at the bottom of the slide, if her mass is 55 kg?

The slide is frictionless, so M.E. is conserved.

Also, the bottom of the slide is the zero level.

Therefore, there is no P.E. at the bottom.

Since Ashley starts from rest,

vi = 0 she has no K.Ei.

G: m = 55 kg, h = 3.0 m g = 10 m/s2

U: vf = ?

E: M.E. i = M.E.f K.E.i + P.E.i = K.E.f + P.E.f

0 + mghi = ½ mv2f + 0

ghm

mghv f 2

2/1

S: vf =

fv

ghm

mghv f 2

2/1

• If you start from rest and end at the bottom (Zero Level) KEI = 0 J and PEf = 0 J.

K.E.i + P.E.i = K.E.f + P.E.f

P.E.i = K.E.f

mghi = ½ mv2

ghi = ½ v2

• If you start from rest and end at the bottom (Zero Level) KEI = 0 J and PEf = 0 J.

K.E.i + P.E.i = K.E.f + P.E.f

P.E.i = K.E.f

mghi = ½ mv2

ghi = ½ v2

ghm

mghv f 2

2/1

Energy conservation occurs

even when acceleration varies.

In the example with the slide, we don’t know the shape of the slide; therefore, acceleration may not be constant. If acceleration is not constant, we can’t use our equations. Since the the slide is frictionless, ME is conserved and the shape plays no part in the ME.

ME is not conserved in the presence of friction.Kinetic Friction causes the KE to

be converted into a non-mechanical form of energy (Heat). This and other forms of energy are difficult to account for and are considered to be ‘lost’.

Section 5-4Rate of Energy

Transfer

PowerThe rate at which energy is transferred.

The rate at which work is done.

Power tells us ‘how fast

work is done.’

WorkPower = ---------

time

W

P = -----

t

Alternative equationUse the work equation and make a substitution.

FdP = ------

t

From Ch 2, the definition of speed: distance moved

per unit of time.

Fvt

dFP

Power Units• From the equation we get:

N-m J P = -------- = ------

s s

We call this a watt (W).

One joule per second equals

one watt.

1000 watts = 1 kilowattA non-metric unit of power

commonly used in commerce and industry is

the horsepower.

•1 Hp = 746 W

Example Problem 9:Rebecca is pushing a lawnmower with a force of 40 N, for 12 m in 10 seconds. (a) what is the work done? (b) what is the power exerted?

(a) Work done:G: F = 40 N

d = 12 mt = 10 s

U: W= ?

E: W = FdS: W=(40 N)x(12

m) S: W = 480 J

B) E: W

P = ----- t

S:P =

S:P =

Example Problem 10:

How much work can a 250 W motor do in 12 seconds?

G: P = 250 W

t = 12 s

U: W = ?

E: W P = -----

t

W = Pt

S:W=

S: W =