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

2. Purdue University, Physics 220
For this example:
vf2 = v02 + 2ax = 2Fx/m
mv2/2 = Fx = W (work)
[N]*[m] = J (joule)
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
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

6. 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

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 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

8. 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
Lecture 9
Purdue University, Physics 220

9. 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

10. Purdue University, Physics 220
Where did the Energy go?
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 did gravity do?
How much work did friction do?
W = mg Dr cos q
= 30  5 cos(90)
 = 0 mg 90 Dr T mg N f
x-direction: SF = ma
T cos(30) – f = 0
f = T cos(30)
W = f Dr cos(180)
= 50 cos(30)  5 cos(180)
 = -217 Joules f Dr
180
Lecture 9
Purdue University, Physics 220

11. Purdue University, Physics 220
Work by Variable Force
Lecture 9
Purdue University, Physics 220

12. Purdue University, Physics 220
Work by Variable Force
Spring: F spring= -k x
Work is the area under the F vs x plot
W by spring force = -1/2 k x2
Lecture 10
Purdue University, Physics 220

13. 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 (energy of motion)
KE = ½ m v2
W = D KE Work-Kinetic Energy Theorem
Lecture 9
Purdue University, Physics 220

14. 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

15. 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
Lecture 9
Purdue University, Physics 220

16. 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
Lecture 9
Purdue University, Physics 220

17. 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
Purdue University, Physics 220

18. 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
Lecture 9
Purdue University, Physics 220