Part ii: predicting terminal velocity – PASCO ME-6828 Dynamics Cart Magnetic Damping User Manual
Page 11
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E x p e r i m e n t 3 : P r e d i c ti n g T e r m i n a l Ve l o c i t y
11
Data Collection
You may need to try several times to complete the following steps successfully. If you
do not get it right, delete your data and try again. The recorded data should show the
motion of the cart only after you release it and before it comes to a complete stop.
There should be about 1 s of recorded data. Use one hand to push the cart and the
other hand to start and stop data recording.
1.
Using a smooth, sweeping motion, push the cart away from the motion sensor
and release it. Make sure that your hand does not prevent the motion sensor from
detecting the cart.
2.
About 0.1 s after releasing the cart, start data recording.
3.
Just before the cart stops, stop data recording.
Analysis
1.
Create a graph showing velocity (on the vertical axis) versus acceleration (on the
horizontal axis).
2.
Apply a linear fit to the data.
According to equation 5, the slope of the best-fit line equals
and the Y-inter-
cept equals
.
Part II: Predicting Terminal Velocity
Theory
If a cart is allowed to roll down an inclined track, its velocity will increase until the
frictional forces acting against the direction of movement equal the gravitational force
acting in the direction of movement. At that point, the net force on the cart is zero, the
acceleration is zero, and the velocity remains constant. This velocity is known as the
terminal velocity,
v
T
.
The gravitational force acting on the cart (in the direction of movement) is
,
where
g = 9.81 m/s
2
and
θ is the angle of incline. At terminal velocity, the net force is
(eq. 6)
The values of
b and f
0
are the same as they were on the level track.
Solving equation 6 gives
(eq. 7)
Analysis
In Part 1, you found the values of
and
. Use these values and equation
7 to predict the terminal velocity of your cart on a track inclined at
θ = 3.0°.
At
θ = 3.0°, v
T
= _________________, prediction
m b
⁄
–
f
0
b
⁄
–
mg
θ
sin
F
net
0
mg
θ
sin
bv
T
f
0
–
–
=
=
for
v
T
0
>
(
)
v
T
m
b
-----g
θ
sin
f
0
b
----
–
=
m b
⁄
–
f
0
b
⁄
–