The Work, and Work-Energy Theorem and

Kinetic EnergyPresented by:

Karen A. AdelanBSE 3

Classical Mechanics

Why Energy?Why do we need a concept of energy?The energy approach to describing motion is

particularly useful when Newton’s Laws are difficult or impossible to use

Energy is a scalar quantity. It does not have a direction associated with it

What is Energy?Energy is a property of the state of a system, not a

property of individual objects: we have to broaden our view.

Some forms of energy:Mechanical:

Kinetic energy (associated with motion, within system) Potential energy (associated with position, within system)

Chemical Electromagnetic Nuclear

Energy is conserved. It can be transferred from one object to another or change in form, but cannot be created or destroyed

Kinetic EnergyKinetic Energy is energy associated with the

state of motion of an objectFor an object moving with a speed of v

SI unit: joule (J) 1 joule = 1 J = 1 kg m2/s2

2

2

1mvKE

Work W

Start with Work “W”Work provides a link between force and energyWork done on an object is transferred to/from

it If W > 0, energy added: “transferred to the

object” If W < 0, energy taken away: “transferred from

the object”

xFmvmv x 20

2

2

1

2

1

Work Unit This gives no information about

the time it took for the displacement to occur the velocity or acceleration of the object

Work is a scalar quantity SI Unit

Newton • meter = JouleN • m = J J = kg • m2 / s2 = ( kg • m / s2 ) • m

xFW )cos(

xFmvmv )cos(2

1

2

1 20

2

Work: + or -? Work can be positive, negative, or zero. The sign of

the work depends on the direction of the force relative to the displacement

Work positive: W > 0 if 90°> q > 0° Work negative: W < 0 if 180°> q > 90° Work zero: W = 0 if q = 90° Work maximum if q = 0° Work minimum if q = 180°

xFW )cos(

Example: When Work is ZeroA man carries a bucket of

water horizontally at constant velocity.

The force does no work on the bucket

Displacement is horizontalForce is verticalcos 90° = 0

xFW )cos(

Example: Work Can Be Positive or Negative

Work is positive when lifting the box

Work would be negative if lowering the box The force would still be

upward, but the displacement would be downward

April 12, 2023

Work Done by a Constant Force The work W done on a system

by an agent exerting a constant force on the system is the product of the magnitude F of the force, the magnitude Δr of the displacement of the point of application of the force, and cosθ, where θ is the angle between the force and displacement vectors:

cosrFrFW

F

II

F

IIIr

F

I

r

F

IVr

r

0IW

cosrFWIV rFWIII

rFWII

net by individual forcesW W

April 12, 2023

Work Done by Multiple Forces If more than one force acts on an object, then the

total work is equal to the algebraic sum of the work done by the individual forces

Remember work is a scalar, so this is the algebraic sum

rFWWWW FNgnet )cos( rFWWWW FNgnet )cos(

net by individual forcesW W

Work and Multiple Forces Suppose µk = 0.200, How much work done on the

sled by friction, and the net work if θ = 30° and he pulls the sled 5.0 m ?

J

mN

smkg

xFmgxN

xfxfW

kk

kkfric

2

2

2

103.4

)0.5)(30sin102.1

/8.90.50)(200.0(

)sin(

)180cos(

J

JJ

WWWWW gNfricFnet

0.90

00103.4102.5 22

Kinetic Energyobject is the energy which it possesses due to its motion.[1] It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest.

In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is ½ mv². In relativistic mechanics, this is only a good approximation when v is much less than the speed of light.

Work-Kinetic Energy Theorem

Is the net work done on an object is equal to the change in the kinetic

energy of the object.

Wnet = ∆KENet work is equal to kinetic energy

• Kinetic energy depends on speed and mass:

KE = ½mv2

Kinetic energy = ½ x mass x (speed)2

KE is a scalar quantity, SI unit (Joule)

• TRY TO SOLVE: Ex. A 7.00 kg bowling ball moves at 3.00 m/s. how much kinetic energy does the bowling ball have? how fast must a 2.24 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? Is the speed reasonable for a table-tennis ball?

Given: the subscript b and t indicate the bowling ball and the table-tennis ball, respectively.Mb = 7.00 kg Mt = 2.24g Vb = 3.00m/sUnknown: KEb = ? Vt = ?

Work-Kinetic Energy TheoremWhen work is done by a net force on an

object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Speed will increase if work is positive Speed will decrease if work is negative

20

2

2

1

2

1mvmvWnet

Work-Energy Theorem

W=KE

W=KEf-KEi

“In the case in which work is done on a system and the only change in the system is in its speed, the work done by the net force equals the change in kinetic energy of the system.”

• The Work-Kinetic Energy Theorem can be applied to non isolated systems

• A non isolated system is one that is influenced by its environment (external forces act on the system)

Work and Kinetic Energy The driver of a 1.00103 kg car traveling on the interstate at

35.0 m/s slam on his brakes to avoid hitting a second vehicle in front of him, which had come to rest because of congestion ahead. After the breaks are applied, a constant friction force of 8.00103 N acts on the car. Ignore air resistance. (a) At what minimum distance should the brakes be applied to avoid a collision with the other vehicle? (b) If the distance between the vehicles is initially only 30.0 m, at what speed would the collisions occur?

April 12, 2023

Work and Kinetic Energy (a) We know Find the minimum necessary stopping distance

Nfkgmvsmv k33

0 1000.8,1000.1,0,/0.35

233 )/0.35)(1000.1(2

1)1000.8( smkgxN

202

10 mvxfk

mx 6.76

Nfkgmvsmv k33

0 1000.8,1000.1,0,/0.35 Nfkgmvsmv k33

0 1000.8,1000.1,0,/0.35

22

2

1

2

1iffricNgfricnet mvmvWWWWW

202

10 mvxfk

233 )/0.35)(1000.1(2

1)1000.8( smkgxN

mx 6.76

Work and Kinetic Energy (b) We know Find the speed at impact. Write down the work-energy theorem:

Nfkgmsmvmx k33

0 1000.8,1000.1,/0.35,0.30

22

2

1

2

1ifkfricnet mvmvxfWW

xfm

vv kf 22

02

2233

22 /745)30)(1000.8)(1000.1

2()/35( smmN

kgsmv f

smv f /3.27