PASCO ME-9486 BALLISTIC CART ACCESSORY - Manual (Page 29)

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012-05460A Ballistic Cart Accessory
Experiment 10: Bombing Run
(Non-Computerized)
EQUIPMENT NEEDED
– Ballistic Cart Accessory (ME-9486) – Clamp-on pulley
– Dynamics Cart and track (ME-9452) – 50-200g mass and hanger
– Drop Rod Accessory (ME-9487) – Scale
– Paper cup (for catching ball) – Plumb bob
– String – Meter stick
Purpose
In this experiment, the distance from the target that a bomber must release the bomb is calculated
and verified. Instead of using a constant-velocity cart, we will use a known acceleration for a
known distance to obtain a repeatable velocity at the time of release.
Theory
We can measure the distance that the cart will accelerate before dropping the ball (d in Figure
10.1) and the height y that the ball will fall. Knowing the mass of the cart and the hanging mass,
we can predict where the ball will land.
First, the velocity of the cart after travelling a distance d from rest will be
v
o
= 2ad
where a is the acceleration of the system. The horizontal distance x that the ball will travel dur-
ing its fall will be
x = v
o
t
y
where ty is the time it takes for the ball to fall:
t
y
=
2y
g
Combining these terms gives us:
x = 2ad
2y
g = 2
ady
g
Now, the acceleration of the system is just
a =
m
m + M
g