Unit IV: Work, Energy, and Momentum

Essential Questions: What is work? How is work related to energy? What is power? What are different types of energy? How is energy conserved?

Energy: The Ability To Do Work

I. WorkA. Work: transfer of energy to an object when the

object moves due to a force1. Work is scalar!

has magnitude only!2. Symbol:

3. Work is also defined as a change in total energy of something

W

TEW

4. Work is also also defined mathematically as Force (F) x Displacement (d)

5. Units for Work:

FdW

FdW mNW m

smkg

2 2

2

smkg

2

2

smkg1 Joule 1 )(J

A 10-N frictional force slows a moving block to a stop after a displacement of 5.0 m to the right. How much work is done on this object?

FdW )5)(10( mN mN 50J50

Example: Work

B. Work Done at Angles F

1. The only part of a force that does work is the part parallel to the direction of movement

2. Formula Becomes:

cosFdW For Horizontal Surfaces

Calculate the work done by a 2.0-N force (directed at a 30° angle to the vertical) to move a 500 gram box a horizontal distance of 400 cm across a rough floor at a constant speed of 0.5 m/s.

cosFdW 60cos)4)(2( mN

Example: Work at an Angle

Journal #17 10/28• Suppose you are dragged to school in the

morning with a force of 282.8 N by a rope with angle of 45° off the ground. If 5000 J of work is done how far did you get dragged?.– Sketch the situation!

II. PowerA. Power: Amount of work done per unit time

1. Power is scalar! has magnitude only

2. Symbol:

3. Power = rate at which work is done

P

4. Power is also also defined mathematically as Work (W) over time (t)

5. Units for Power:tWP

tWP

sJ

1 sJ

Watt11W

Note that kilowatts (kW) are often used to keep numbers smaller

6. There is one more way to express Power

FdW

tWP

tWP

tFd

vFP

Formulas In Your Reference Tables!!

A 60 kg box of squirrels is pushed for 10 meters toward a cliff with a force of 200 Newtons. It takes 20 seconds to reach the edge of the cliff.

What is the work done? What is the average velocity of the box? What is the Power generated during the push? What is the Power generated during the push?

(use a different formula!)

Example: Power

B. Graphs of Work and Power1. Work vs. Displacement

Displacement (m)

Wor

k Do

ne

(J)

Relationship:“As the displacement increases, the work done increases”

Type of Relationship:

DIRECT

Slope of Work vs. Displacement

dW

runriseSlope

xy

F

Displacement (m)

Wor

k Do

ne

(J) Units:

dW

mmN

mJ

N

2. Power vs. Time

Time (s)

Powe

r (W

atts

) Relationship:“As time passes, the power generated decreases”

Type of Relationship:

INDIRECT

Journal #17 10/29A jaguar does 3000 J of work dragging a capybara toward its den.

• If the distance from the kill to the den is 30 meters, how much force was exerted?

• How much power was developed if it took 40 seconds to move the rodent?

• How could the power generated by the jaguar be increased?

III. Forms of EnergyA. Potential Energy: possessed by an object due

to its position or condition1. Gravitational: gained by doing work to raise an object to a height above Earth’s surface

a. Work done lifting an object:

FdW b. The force exerted is equal to the weight of the object when lifted vertically

gFF mg

dFW gSo:

Work Done (W)= Change in Potential Energy

(ΔPE)mghPE Displacement is just height lifted (h)

c. Units for Gravitational Potential Energy

mghPE

))()(( 2 mkgPEsm

))(( 2

2

smkgPE mN or

)(JJoulesPE

The jaguar from earlier decides to drag the dead 50 kg rodent up into a tree instead.

• If the tree is 25 meters tall, how much potential energy does the rodent now have?

• How much work did the jaguar do in dragging the rodent upward?

• How much force was exerted in this process?

Example: Potential Energy

Journal #18 10/30A crane lifts a 90 kg box of chipmunks up to a height of 200 m.

• How much potential energy does the box now have?

• What is the work done by the crane?• What is the lifting force from the crane (tension)?• What is the weight of the box?

2. Elastic Potential Energy: energy stored in an object or device by stretching or compressing it (doing work)

a. How much energy can be stored depends on the constant (k) of the material

Units: Newtons per meter (N/m)b. Stretch is directly

proportional to force applied

kxFs Hooke’s Law

Example: Hooke’s Law• A spring with a constant of 40 N/m is stretched

20 cm. What is the force that stretched the spring?

c. Potential Energy of a Spring (PEs) is proportional to the constant (k) and the stretch/compression (x) squared

221 kxPEs

Small change in length = lots of potential energy change

Elongation (m)

Pote

ntia

l Ene

rgy

(J)

Example: Spring PE• A spring with a constant of 40 N/m is stretched

20 cm. What is the Potential Energy stored that in the spring?

• What is the work done on the spring?

B. Kinetic Energy: energy possessed by an object due to its movement1. Dependent on mass and velocity!

2. Mathematic Definition:

Formula In Your Reference Tables!!

221mvKE

3. Units for Kinetic Energy

221mvKE

2))(( smkgKE

))(( 2

2

smkgKE mN or

)(JJoulesKE

4. Graph of Kinetic Energy vs. Speed

Speed (m/s)

Kine

tic E

nerg

y (J)

Relationship:“As the speed of an object increases, its kinetic energy increases (by a lot)”

Type of Relationship:

DIRECT SQUARED

What is the kinetic energy of a 45.5 kg cannonball that is fired toward a nearby squirrel with a velocity of 50 m/s?

Example 1: Kinetic Energy

IV. Conservation of EnergyA. Energy changes forms between kinetic and

potentialB. Law of Conservation of Energy:

Energy cannot be created nor destroyedC. When friction/air resistance are ignored, work

done to change energy of an object or system is the SAME regardless of path taken

D. Change in Potential Energy (ΔPE) is equal to the change in Kinetic energy (ΔKE) in an ideal system: PEKE

KEPEET Total Energy (ET) Remains the SAME!

Total Energy Is Conserved!

• Example: Pendulum!

A crane lifts a 90 kg box of chipmunks up to a height of 200 m.

What is potential energy of the box? When the box is dropped, what will be the kinetic energy of the box before it hits the ground? What will be the final velocity of the box? Calculate the kinetic energy of the box.

Example 2: Kinetic Energy

Journal #18 1/12• Rico slides a 60 kg crate of pureed squirrels up

an inclined ramp 2.0 m long onto a platform1.0 m above floor level. A 400 N force parallel to the ramp is needed to slide the crate up the ramp at a constant speed.– How much work does Rico do in sliding the

crate up the ramp?– How much work would be done if Rico

simply lifted the crate straight up from the floor to the platform?

C. Thermal Energy: Heat resulting from kinetic energy of particles within an object

D. Internal Energy: total energy possessed by particles within an object

E. Nuclear Energy: released by splitting or combining nuclei of atoms (fission & fusion)

F. Electromagnetic Energy: associated with electric and magnetic fields

QSymbol: