Lecture 16
Conservative and NonConservative
Forces
Examples.
ACT: Falling objects
Three objects of mass
m
are dropped from a height
h
. One
falls straight down, one slides down a frictionless incline
and one swings at the end of a pendulum. What is the
relationship between their speeds when they reach the
ground?
v
F
P
I
A.
F
>
I
>
P
B.
F
>
P
>
I
C.
F
=
I
=
P
DEMO: Two
tracks
In all three cases, the only force doing work
is gravity
→
mechanical energy is conserved.
Same final
speed
i
0
Em
g
=+
2
f
1
0
2
Oscillations
A glider of mass
m
= 0.5 kg on a horizontal frictionless
surface is attached to a spring with
k
= 200 N/m. The
glider is pulled 3 cm away from the equilibrium position and
released. Find its speed when the spring has been
compressed 1 cm.
x
2
= 1 cm
=
0
1
=
–
3 cm
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentA glider of mass
m
= 0.5 kg on a horizontal frictionless surface is attached to a
spring with
k
= 200 N/m. The glider is pulled 3 cm away from the equilibrium
position and released. Find its speed when the spring has been compressed 1 cm.
x
2
= 1 cm
=
0
1
=
–
3 cm
22
111
11
Em
vk
=+
222
0
2
12
2
kx
mv
()
21
2
vx
=−
2
(200 N/m)
0.03
0.01 m
0.57 m/s
0.5 kg
=
Careful with
the units
DEMO:
Glider on a
track
EXAMPLE: Vertical spring
A 50g ball is shot by a vertical spring compressed over a
distance x = 2.0 cm. It reaches a height
h =
2.5 m above
the initial position. Determine the spring constant
.
h
Mechanical energy of the ball:
+
v
g
(with the appropriate choice of zero
potential energies, see figure)
2
initial
1
Before the shot:
(
0)
2
Ek
==
top
At the top:
(
0)
Emgh
2
1
2
mgh
=
2
2
2(0.05 kg)(9.8 m/s )(2.5 m)
6100 N/m
(0.02 m)
1
U
= 0
el
= 0
2
2
=
DEMO:
Hopperpopper
and ball
Mechanical energy with
nonconservative forces.
In a system where only conservative forces are doing work,
mechanical energy is conserved:
0
E
∆=
If both conservative and nonconservative forces are
doing work:
K
W
∆
=
net
c

n
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 Fall '06
 Johnson
 Physics, Force, Friction, Mass, Potential Energy, Wfriction

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