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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
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