PASCO ME-9430 Dynamics Cart with Mass - Manual (Page 7)

012-04840E Dynamics Cart
3
®
Purpose
In this lab, the Dynamics Cart will be used to investigate one dimensional accelerated
motion. You will launch the cart over the floor using the built-in spring plunger. The cart
will “decelerate” over the floor under the combined action of rolling friction and floor slope.
You will be able to establish whether or not the acceleration of the cart is constant. This will
be done by initially assuming a constant acceleration and then by examining the results to
see if they are consistent with this assumption.
Theory
The cart will be allowed to roll to a stop. The distance covered, D, and the total elapsed
time, T, from launch to stop will be measured and recorded. The average velocity over this
interval is given by:
v
av
= (EQN–1)
If the acceleration of the cart is constant as it rolls to a stop over the floor, then the initial
instantaneous velocity of the cart at the final moment of launch is given by:
v
0
= 2v
av
= (EQN–2)
And the value of the acceleration would be given by:
a = = = – (EQN–3)
If the acceleration and v
o
are known, then the time, t
1,
required to cover the distance (d) to
some intermediate point (i.e. short of the final stopping point!) can be calculated by applying
the quadratic formula to:
d = v
0
t
1
+ 1/2at
1
2 (EQN–4)
Calculated values of t
1
will be compared with directly measured values. The extent to which
the calculated values agree with the directly measured values is an indication of the con-
stancy of the acceleration of the cart.
Note your theoretical values in Table 1.1.
Experiment 1: Kinematics
(Average vs. Instantaneous Velocities)
Figure 1.1
EQUIPMENT NEEDED:
– Dynamics Cart (ME-9430)
– Metric tape (SE-8712)
– Stopwatch (SE-8702)
∆ v
t
0 – v
0
T
2D
T
2
D
T
2D
T
∆