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?
h
v
F
v
P
v
I
A.
v
F
>
v
I
>
v
P
B.
v
F
>
v
P
>
v
I
C.
v
F
=
v
I
=
v
P
DEMO: Two
tracks
In all three cases, the only force doing work
is gravity
→
mechanical energy is conserved.
Same final
speed
i
0
E
mgh
=
+
2
f
1
0
2
E
mv
=
+
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
x
=
0
x
1
=
–
3 cm
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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
x
=
0
x
1
=
–
3 cm
2
2
1
1
1
1
1
2
2
E
mv
kx
=
+
2
2
2
2
2
1
1
2
2
E
mv
kx
=
+
0
2
2
2
1
2
2
1
1
1
2
2
2
kx
mv
kx
=
+
(
)
2
2
2
1
2
k
v
x
x
m
=
−
(
)
2
2
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
k
.
h
x
Mechanical energy of the ball:
=
+
+
2
2
1
1
2
2
E
mv
mgh
kx
(with the appropriate choice of zero
potential energies, see figure)
2
initial
1
Before the shot:
(
0)
2
E
kx
v
=
=
top
At the top:
(
0)
E
mgh
v
=
=
2
1
2
kx
mgh
=
2
2
2(0.05 kg)(9.8 m/s
)(2.5 m)
6100 N/m
(0.02 m)
k
=
=
h
x
1
U
g
= 0
U
el
= 0
2
2
mgh
k
x
=
DEMO:
Hopperpopper
and ball
Mechanical energy with
nonconservative forces.
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 Fall '06
 Johnson
 Physics, Force, Friction, Mass, Potential Energy, Wfriction

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