1. Work and Kinetic Energy
PHYSICS 220
Lecture 9
Work and Kinetic Energy
Lecture 9
Purdue University, Physics 220

2. Purdue University, Physics 220
Newton’s Second Law leads to definitions of work and energy
The connection between force and energy is work
Lecture 9
Purdue University, Physics 220

3. Purdue University, Physics 220
Work and Energy
Work: Transfer of Energy by Force
W = |F| |r| cos
W depends on the direction of the force relative to the displacement
Lecture 9
Purdue University, Physics 220

4. Purdue University, Physics 220
Work by Constant Force
Only component of force parallel to direction of motion does work!
W = F Dr cos q F q Dr F
WF > 0: 0< q < 90 : cos(q) > 0 Dr F
WF = 0: q =90 : cos(q) =0 Dr F
WF < 0: 90< q < 270 : cos(q) < 0 Dr F
WF > 0: 0< q < 90 : cos(q) > 0
Lecture 9
Purdue University, Physics 220

5. Purdue University, Physics 220
iClicker
You toss a ball in the air. The work done by gravity as the ball goes up is:
A) Positive B) Negative C) Zero
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6. Purdue University, Physics 220
Work by Constant Force
Example: You pull a 30 N chest 5 meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force? T mg N f
W = T Dx cos q
= (50 N) (5 m) cos (30)
= 217 Joules
50 N 30
Lecture 9
Purdue University, Physics 220

7. Purdue University, Physics 220
Question
You are towing a car up a hill with constant velocity. The work done on the car by the normal force is:
A) positive B) negative C) zero W N V T
Normal force is perpendicular to direction of displacement, so work is zero.
Lecture 9
Purdue University, Physics 220

8. Purdue University, Physics 220
Question
You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is:
A) positive B) negative C) zero W T N V
Gravity is pushing against the direction of motion so it is negative.
Lecture 9
Purdue University, Physics 220

9. Purdue University, Physics 220
Question
You are towing a car up a hill with constant velocity. The work done on the car by the tension force is:
A) positive B) negative C) zero W T N V
The force of tension is in the same direction as the motion of the car, making the work positive.
Lecture 9
Purdue University, Physics 220

10. Kinetic Energy: Motion
Apply constant force along x-direction to a point particle m
W = Fx Dx
= m ax Dx
= ½ m (vf2 – v02)
Work changes ½ m v2
Define Kinetic Energy KE = ½ m v2
W = D KE Work-Kinetic Energy Theorem
Lecture 9
Purdue University, Physics 220

11. Example: Block with Friction
A block is sliding on a surface with an initial speed of 5 m/s. If the coefficient of kinetic friction between the block and table is 0.4, how far does the block travel before stopping? x y mg N f
y-direction: F=ma
N-mg = 0
N = mg
Work
WN = 0
Wmg = 0
Wf = f Dx cos(180)
= -mmg Dx
W = D KE
-mmg Dx = ½ m (vf2 – v02)
-mg Dx = ½ (0 – v02)
mg Dx = ½ v02
Dx = ½ v02 / mg
= 3.1 meters
On transparency
5 m/s
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12. Purdue University, Physics 220
Falling Ball Example
Ball falls a distance of 5 meters. What is its final speed?
Only force/work done be gravity
Wg = m ½ (vf2 – vi2)
Fg h = ½m vf2
mgh = ½m vf2
Vf = sqrt( 2 g h ) = 10 m/s mg
Lecture 9
Purdue University, Physics 220

13. Work: Energy Transfer due to Force
Force to lift trunk at constant speed
Case a Ta – mg = 0 Ta = mg
Case b 2Tb - mg =0 or Tb = ½ mg
But in case b, trunk only moves ½ distance you pull rope
Work is same in both!
Get demo Tb mg Ta mg
W = mgh
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14. Purdue University, Physics 220
Work Done by Gravity 1
Example 1: Drop ball
Wg = (mg)(s)cos
s = h
Wg = mghcos(00) = mgh
y = yf-yi = -h
Wg = -mgy S
Yi = h
Yf = 0 mg y x
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Work Done by Gravity 2
Example 2: Toss ball up
Wg = (mg)(s)cos
s = h
Wg = mghcos(1800) = -mgh
y = yf-yi = +h
Wg = -mgy
Yf = h
Yi = 0 mg S y x
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16. Purdue University, Physics 220
Work Done by Gravity 3
Example 3: Slide block down incline
Wg = (mg)(s)cos
s = h/cos
Wg = mg(h/cos)cos
Wg = mgh
y = yf-yi = -h
Wg = -mgy h  mg S
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Work Done by Gravity
Depends only on initial and final height!
Wg = -mg(yf - yi) = -mgy
Independent of path
If you end up where you began, Wg = 0
Define: Potential Energy PEgrav = mgy
Wg = - PEgrav
We call this a “Conservative Force” because we can define a “Potential Energy” to go with it.
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Purdue University, Physics 220

18. Purdue University, Physics 220
Energy
Energy is “conserved” meaning it can not be created nor destroyed
Can change form
Can be transferred
Total Energy of an isolated system does not change with time
Types
Kinetic Energy
Potential Energy
Rest Energy (E=mc2)
Thermal Energy
… …
Units: Joule (J) = N m = kg m2 / s2
Maybe do example of conservation (like cookies) and counter example like acceleration
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19. Purdue University, Physics 220
iClicker
A box is pulled up a rough (m > 0) incline by a rope-pulley-weight arrangement as shown below. How many forces are doing (non-zero) work on the box?
A) 0 B) C) D) E) 4
Lecture 9
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20. Purdue University, Physics 220
Solution
Draw FBD of box: N
Consider direction of motion of the box v T
Any force not perpendicular to the motion will do work:
mg does negative work f
N does no work (perp. to v)
T does positive work
3 forces do work mg
f does negative work
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21. Purdue University, Physics 220
There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law; it is exact, so far we know. The law is called conservation of energy; it states that there is a certain quantity, which we call energy, that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.
Richard Feynman
Lecture 9
Purdue University, Physics 220