Download Work and Energy Conservation of Mechanical Energy W k b N ti f

Common Exam 2
During class (1 - 2:55 pm) on 6/14, Tue
Room: 412 FMH (classroom)
Bring scientific calculators
E
Exam
covers all
ll lectures
l t
after
ft common exam 1.
1
Review session: Monday during class
1
Work and Energy
Conservation of Mechanical Energy
More examples on conservation of mechanical Energy
W k by
Work
b Non-conservative
N
ti force
f
Power
2
1
A
ΔU g = mgh
g A − mgh
g B = mgg (hA − hB ) = mgg Δh
B
iClciker: True or false?
(a), (b), and (c) have the same answer.
A) True
B) False
C) N.E.I.
NEI
3
Example: Pendulum
2 m rope
30 degree
V_i=0
What is the speed at the bottom?
4
2
Example. A car with its engine off costs along a straight highway,
which goes uphill. How far along the highway will the car go before
its stops, if its initial speed was 30 m/s, and the slope is 15o? The
tires roll, not skid.
5
How much work is done by a person lifting a 2.0-kg
object from the bottom of a well at a constant speed of
2.0 m/s for 5.0 s?
6
3
Work done on a system by non
non-conservative force
What if non-conservative forces do work on an object, in addition
to conservative force?
Non-conservative force: friction force, tension, normal, applied force…
Example: Surface with friction
Normal force
Friction force
Displacement
Gravitational force
First, let’s review sliding on surface without friction
Normal force
v1
Height
Displacement
h1
h2
0
Gravitational force
Emech ,1 = Emech ,2
Æ
v2
Æ
1
1
mgh1 + mv12 = mgh2 + mv22
2
2
Emech ,2 − Emech ,1 = ΔEmech = 0
4
Now, with friction……
Normal force
Height Friction force
v1
Displacement
h1
h2
Gravitational force
0
v2
v2
with friction is smaller than
Æ Emech ,2
v2
without friction.
− Emech ,1 = ΔEmech ≠ 0
Relation between ΔEmech & friction force?
Generally,
ΔEmech = Wnon −conservative
Æ Mechanical energy changes
ΔEmech = W friction
(see text for proof)
Work done on a system by non
non-conservative force
If non-conservative forces do work on an object, in addition to
conservative forces,
Æ Mechanical energy changes
b th
by
the amount
m nt of
f work
k done
d n by
b the
th non-conservative
n n ns
ti f
force.
ΔEmech = Emech, f − Emech ,i = Wnon −conservative
Emech = K + U
5
Example: Surface with friction
K1 = 0 J
Displacement = 5 m
K2 = ?
Height change
= 3m
Mass of the dog = 10 kg
Friction force = 10 N
Find the final kinetic energy,
K2 = ?
Example: A skier stars from rest at the top of a frictionless incline
of height 20 m . At the bottom of the incline, the skier encounters
a horizontal surface where the μ k =0.21 . How far does the skier
travel on the horizontal surface before coming to rest?
iClicker 1: In this problem, work done by normal force is _____ .
iClicker 2: In this problem, work done by gravity force is _____ .
iClicker 3: In this problem, work done by friction force is _____ .
(a) positive, (b)zero, (c)negative
12
6
7. A person pulls a sled with load from rest. The total mass
of the sled with load is 50kg,
and the person exerts a force of 1.2x102 N on the sled
by pulling on the rope with angle 30 degree. (u_k =0.2)
What is the kinetic energy of the sled after he pulls
the sled 5 m?
iClicker Quiz
In this problem, Magnitude of the normal force is mg.
(A) true (B) false
13
A 12-kg projectile is launched with an initial vertical
speed of 20 m/s. It rises to a maximum height of 18 m
above the launch point. How much work is done by the
dissipative (air) resistive force, which is a nonconservative force, on the projectile during this ascent?
14
7
Many types of energy
Mechanical energy, thermal energy, chemical energy,
light energy, electric energy, magnetic energy,………
General principle of Conservation of Energy
Total energy of an isolated system is conserved.
P =
In 2D,
ΔW
Δt
=
F Δx
= Fv
Δt
(in 1D)
Instantaneous Power:
G G
= F v cos θ F ,v
16
8
Work done by a constant force
G G
G G
W = F d cos θ F ,d ≡ F ⋅ d
Force
θ
Di l
Displacement
t
Instantaneous Power by a force
G G
G G
P = F v cos θ F ,v ≡ F ⋅ v
Force
θ
Velocity
17
A weightlifter, is able to lift 250 kg 2.00 m in 2.00 s.
What is his power output?
18
9
A jet engine develops 1.0 x 10^5 N of thrust in moving an
airplane forward at a speed of 250 m/s. What is the power
developed by the engine?
19
10