cceleration in One Dimension
PHYS 0212 BallisticMotion
1
Bench Top
Ballistic
Launcher
Impact
Point
Start
Point
Launch
Point
Plumb
Bob
A
1
h
2
h
Impact Distance
h
1
= Height of the center of mass above the launch point
h
2
= Height of the launch point above the table
Ballistic Motion
PHYS 0212 BallisticMotion
2
The basic procedure:
3. Measure the impact distance as a function of height
h
2
.
1. Repeatedly measure the impact distance
for a fixed height
h
2
.
A
2. Calculate the mean and standard deviation of the impact distance
.
A
4. Plot
versus
h
2
.
2
A
We can find the impact distance of the ball if we know its velocity at the launch
point.
Horizontal (
x
) and vertical (
y
) motions are independent, so we can write out the
equations of motion for constant acceleration.
x
direction
y
direction
2
1
0
0
2
x
x
x
x
v t
a t
=
+
+
2
1
0
0
2
y
y
y
y
v
t
a t
=
+
+
0
0
0
0
0
x
x
x
v
v
a
=
=
=
0
2
0
0
y
y
y
h
a
g
v
=
=
= −
At the launch point
(
assuming the initial
velocity is completely
horizontal
)
}
{
PHYS 0212 BallisticMotion
3
x
direction
y
direction
(
)
( )
2
1
0
0
2
2
1
0
2
0
0
x
x
x
x
v t
a t
x
v
t
t
=
+
+
=
+
+
( )
(
)
2
1
0
0
2
2
1
2
2
0
y
y
y
y
v
t
a t
y
h
t
g t
=
+
+
=
+
+
−
0
x
v t
=
2
1
2
2
y
h
gt
=
−
Bench Top
A
Impact Distance
2
h
When the ball reaches the impact point:
and
0
x
y
=
=
A
0
v t
=
A
2
1
2
2
0
h
gt
=
−
The time
t
is the same in
both of these equations.
0
v
PHYS 0212 BallisticMotion
4
0
2
2
2
0
t
v
t
v
=
=
A
A
2
1
2
2
2
0
h
g
v
=
A
0
v t
=
A
2
1
2
2
0
h
gt
=
−
Eliminate
t
from both equations:
2
2
2
0
2
h
v
g
=
A
Solve for
2
A
2
1
2
2
h
gt
=
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 Spring '08
 Naples
 Physics, Center Of Mass, Energy, Kinetic Energy, Mass, impact distance

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