1. Unit 3: Energy and Momentum
Lesson 1: Work

2. Definition of Work: 1D: work = force x distance
2D: work = parallel force x distance
W = F װ • d
UNIT of MEASURE: Joules

3. W = F װ • d = 100 cos70 x 30 = 1030 J b) f = 100 cos70 = 34.2 N
Example 1: Damian gets a summer job mowing lawns. His lawnmower’s handle makes an angle of 70°with the ground. A 100 N force is applied causing the 20 kg machine to cover 30 m at a constant speed.
Find:
A) The work done by Damian
B) The work done by friction
C) The work done by the normal force N
W = F װ • d
= 100 cos70 x 30
= 1030 J f
I do – 15 min P
b) f = 100 cos70 = 34.2 N
W = x 30
= J mg
c) Nװ = 0 W= 0
Note: net work done is 0!

4. Brain Break!

5. Fnet = 0 N = mg cos θ = 193 N f = uN = 77.2N P = f + mg sin θ = 111 N
Example 2: Morgan pushes a 20 kg pile of textbooks 15 m up a rough ramp (u=0.4), inclined at 10 degrees, at a constant speed.
Find the work done by each individual force and by the net force. N P
Fnet = 0
N = mg cos θ = 193 N
f = uN = 77.2N
P = f + mg sin θ = 111 N f mg
We do – 15 min
Wnet = 0
WN = N װ • d = 0
Wf = -f • d = J
Wp = P • d = 1670 J
Wg = -mg sin θ • d = -510 J
Interpretation
Morgan does 1670 J of work.
1160 J is dissipated by friction (heat).
510 J is converted to gravitational
potential energy.

6. Practice:
Do #1 and 2 on pg. 82
10 min

7. Unit 3: Energy and Momentum
Lesson 2: The Work-Energy Theorem

8. Work – Energy Theorem W = ΔKE “Work Energy Theorem”
Fnet
| d | Vo → V
W = ΔKE
“Work Energy Theorem”
W = work done by NET force
KE = ½mv2

9. Example 1: Famous astronaut Dane VeldBOOM is making a weekend trip to the moon. Find the thrust force (assumed constant) needed to accelerate his 600 kg rocket from 100 m/s to 150 m/s over 1.5 km (in space).
W = ΔKE
F • d = ½mv2 - ½mvo2
F (1500) = ½(600)(150)2 - ½(600)(100)2
F (1500) = 3.75 x 106 J
F = 2500 N
I do – 5 min

10. Video: World’s Fastest Crash Test
5 min

11. A) the work done by the wall on the car
Example 2: A 600 kg smart car smashes into a concrete wall at 20 m/s, crumpling 0.8 m.
Find:
A) the work done by the wall on the car
B) the average force on the car during the collision
0.8m
I do – 10 min
W = ΔKE
= 0 - ½mv2
= 0 – ½(600)(20)2
= J
b) W = F • d
F = W/d = / 0.8
= N

12. Conservation of Energy
For an object under the influence of gravity, where no other forces do any work:
E.g. – projectile
– pendulum m V2 h2 V1 h1
Total mechanical energy = PE + KE
is CONSERVED! (if no other forces do work)
A famous example of
this is Newton’s cradle:

13. Example 3: Tarzan, a 75 kg “ape-man” runs along a branch at 3
Example 3: Tarzan, a 75 kg “ape-man” runs along a branch at 3.0 m/s, grabs a vine, and swings away. The branch is 5.0 m high.
Find:
The speed of Tarzan as he barely misses the ground
The maximum height he swings to
His speed when 2.0 m above the ground
5.0m
The vine is massless and unstretchable and there is no air resistance.
I do – 5 min
PE 1+ KE1 = PE2 + KE2
Define PE = 0 at ground level
The vine does no work (always perpendicular to direction of motion)
(75)(9.8)(5) +½(75)(3)2 = 0 + ½(75)v2
v2 = 2[(9.8)(5) + ½(3)2]
v = 10.3 m/s

14. b) (75)(9.8)(5) + ½(75)(3)2 = (75)(9.8)h + 0 4012.5 = (75)(9.8)h
5.0 m
b) (75)(9.8)(5) + ½(75)(3)2 = (75)(9.8)h + 0
= (75)(9.8)h
h = 5.46 m
10 min
c) Etotal = ½mv2 + mgh
= ½(75)v2 + (75)(9.8)(2)
37.5v2 =
v = 8.2 m/s

15. Recommended Questions:
Energy Practice Problems #2, 11-13, and 18
15 min