Common Exam 3
8:30-9:45 am Friday, Nov. 20th (Arrive by 8:15 am)
1
Work and Energy
Conservative vs. Non-conservative forces
Gravitational Potential Energy
Last class…
Spring force and spring potential energy
Conservation of Mechanical Energy
Work by Non-conservative force
Today…
Power
2
1
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, force from a hand, …
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
2
Now, with friction……
Normal force
Height Friction force
v1
Displ
Displacement
m nt
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 force,
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
3
Example: Surface with friction
K1 = 45 J
Displacement = 2 m
K2 = ?
30o
Mass of the dog = 10 kg
Friction force = 10 N
Find the final kinetic energy, K2.
Thermal energy and Work done by friction force
Mechanical energy is reduced by friction force.
Where has this mechanical energy gone?
Observation : Friction heats up the object and the surface
Some Mechanical Energy is converted to Thermal Energy
ΔEthermal = W friction = −W friction = −ΔEmech
ΔEthermal + ΔEmech = 0
Æ
Etotal = Emech + Ethermal
is conserved.
Total energy of the whole system, dog + surface, is conserved.
4
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.
(in 1D)
In 2D & 3D, Power:
r r
= F v cos θ F ,v
10
5
Work done by a force
r r
r r
W = F d cos θ F ,d ≡ F ⋅ d
Force
θ
Di l
Displacement
t
Power done by a force
r r
r r
P = F v cos θ F ,v ≡ F ⋅ v
Force
θ
Velocity
11
Example
Killer whales are known to accelerate very fast.
Calculate the average power a killer whale
with mass 8000 kg would need to generate to reach
a speed of 12.0 m/s from rest in 6.0 s.
Assume water resistance is negligible.
12
6