Chapter 6Work and Energy6.1 – Work

Work Formula & UnitsPositive & Negative Work

6.2 – Work-Energy Theorem & Kinetic EnergyKE Formula & Units

6.3 – Gravitational Potential EnergyGPE FormulaPositive & Negative Work

6.4 – Conservation of EnergyTotal Mechanical Energy

6.5 – PowerPower Formula

Work is done on an object whenever a force is applied parallel to the displacement.

6.1 – Work Done by a Constant Force

Work = Force x Displacement

Less work is done on the object in bottom figure.

( cos )W F s

displacement (m) force (N) work

(N·m or Joule)

( cos )W F s

θ = 0°; cosθ =1W = F(s)

θ = 90°; cosθ = 0W = 0

θ = 180°; cosθ = -1W = - F(s)

θ = 270°; cosθ = 0W = 0

Block is moving this way

Person is doing positive work

on the barbell when lifting.

Person is doing negative work

on the barbell when lowering

Work can be positive or negative, but it is NOT a vector.

Work is measured in Joules (Newton-meters) or ft-lbs

1. Lifting a weight up off the floor.

Are you doing work on the object?

2. Pushing a truck as hard as you can but the truck doesn’t move

3. Carrying books across a room.

4. Lowering a barbell during a bench-press rep.

5. Gravity pulling a ball down to earth.

6. Gravity pulling on a book resting a table.

YES

YES, negative work

YES

NO

NO

NO

For now, a good way to know if work is done is to see if the PE or KE of the

object is changed.

Work will cause a change in energy of the object.

Ch. 6 Homework #1

Ch. 6Problems #1-5 (p. 180)

Energy - The ability to do work; measured in Joules

Kinetic Energy - Energy due to motion

21

2KE mv

mass (kg)

velocity(m/s)

6.2 – Work-Energy Theorem & KE

F ma Fd W mad

2 20 2fv v ad

2 20

2fv v

ad 2 2

0

2fv v

W m

2 21 102 2fW mv mv

f iW KE KE

The Work-Energy Theorem -

A net external force on an object changes the KE of the object.

The change in KE of the object equals the work that was done on the object

W = ΔKE

f iW KE KE

Ch. 6 Homework #2

Ch. 6Problems #12,13,15,17

p. 181

Potential Energy -

Energy due to relative position

Elastic Potential EnergyElectrical Potential Energy

Gravitational Potential Energy

6. 3 - Gravitational Potential Energy

Work done by the force of gravity

0( cos 0 )( )grav fW mg h h

( cos )W F s

gravW mgh

height difference (m)

Gravitational Potential Energy

height (m)

PE mgh

The work done by gravity does not depend on the path taken, only the

height difference.

The total mechanical energy (E) of an object remains constant, neglecting frictional forces.

E = KE + PE

6. 4 – Conservation of Mechanical Energy

Einitial = Efinal

The Kingda Ka is a giant roller coaster with a vertical drop of 127 m. Suppose that the coaster has a speed of 6.0 m/s at the top of the drop. Neglect friction and air resistance and find the speed of the riders at the bottom in miles/hour

Chapter 6 Homework #3

Ch. 6Problems #25,26,28,35,32,36page 182

Power - the rate at which work is done.

1 horsepower = 550 ft-lbs/sec = 745.7 watts

(joules) (watts) =

(sec)

WorkAverage Power

time

6. 5 – Power

Conservation of Energy Lab

When block is moving up or down at constant velocity, the net force is zero.

Fup = Fgrav + fk Fdown = Fgrav - fk

Fup + Fdown = 2 (Fgrav )

Conservation of Energy Lab

4. Work = Fgrav x length

1. W = mg

2. Fgrav = (Fup + Fdown) /2

3. Fgrav = Wsinθ

5. ΔPE = mgh

6. Workactual = Fup x length

Ch. 6 Equations

( cos )W F s21

2KE mv

f iW KE KE

gravW mgh (joules)

(watts) = (sec)

WorkAverage Power

time

E = KE + PE

Einitial = Efinal