PASCO ME-6828 Dynamics Cart Magnetic Damping - Manual (Page 9)

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M E - 6 8 2 8 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
9
Experiment 3: Predicting Terminal Velocity
Introduction
In this experiment, you will study the motion of a magnetically damped cart. First,
you will discover the relationship between the velocity and acceleration as it comes to
a stop after being pushed on a level track. Using this relationship, you will predict the
cart’s terminal velocity on a inclined track. Finally, you will test your prediction.
Part I: Acceleration versus Velocity
Theory
The magnetic drag force, f
m
, is proportional to (and in the opposite direction of)
velocity v
(eq. 1)
where b is a positive constant.
On a level track, assuming no other sources of friction, f
m
is the only force (along the
axis of movement) acting on the cart. Therefore, by Newton’s second law
(eq. 2)
where m is the mass of the cart and a is the acceleration. (Note that f
m
and a are not
necessarily constant over time.)
The combination of equations 1 and 2 gives the relationship between a and v
(eq. 3)
In a graph of v versus a, the slope will equal .
Equipment Part Number
Dynamics Cart Magnetic Damping ME-6828
Motion Sensor PS-2103A or similar
Cart
1
ME-6950, ME-9430, or ME-9454
Aluminum Track
1
ME-6953 or similar
IDS Pivot Clamp
1
ME-9810
Large Table Clamp ME-9472
90 cm Rod ME-8738 or similar
Angle Indicator
2
ME-9495
1 These items are components of many PASCO dynamics systems.
2 Or other way to measure track angle
f
m
bv – =
f
m
ma =
v
m
b
----- a – =
m b ⁄
–