Experiment 10: Impulse and Momentum
Aim:
To investigate the relationship between impulse and momentum.
Theory:
To change an object's motion we need to apply a force for a period of time. This quantity of
force x time is known as impulse. For an object experiencing a constant force we can find an
equation for impulse by using Newton's Second law (F=ma) and the equations of motion as
follows
I  Ft  mat
 mv2  mv1
 P
Where F is the force acting on the body, P is the change in momentum, m is the mass of the
body and v1, v2 are the velocities of the body before and after impulse. Note that momentum,
force, acceleration and velocity are all vector quantities and so impulse has the same direction
as the force that produced it.
In this experiment a trolley collides with a force sensor and the change in momentum is
compared to the impulse.
The impulse is found by calculating the area under the force vs time graph (the integral of the
force) measured by the sensor.
A photo gate is used to measure the velocities of the trolley before and after the collision.
Equipment: Force and photo gate sensors connected to an interface or data logger, linear
airtrack and glider (or ramp and dynamics trolley) and a computer.
Data Logger Setup:
 Input 1: Photo Gate
 Input 2: Force Sensor
 Samples: 40000
 Rate: 10000 / Sec
Phil Jones
The Logical Interface
www.logint.com.au
Method:
I.
Setup the equipment as shown
II.
Connect the data logger or interface to the computer and start the software.
III.
Place the glider or trolley on the track as shown in the diagram with a glider flag
(10 cm).
IV.
Start logging and immediately push the trolley towards the force sensor. Make
sure that the initial push is strong enough: after the collision the trolley must pass
back through the photo-gate so that its velocity after the collision can be
calculated.
V.
Measure the mass of the trolley. Record this value.
Phil Jones
The Logical Interface
www.logint.com.au
Analysis:
1. Calculate the impulse:
 Display a graph of force vs time. The area under the curve is the Impulse (see
below).
Dual-Range Force Sensor N (+/-50) vs Time
50.71
5.00
4.50
4.00
40.62
3.50
3.00
30.54
2.50
2.00
1.50
20.46
1.00
0.50
0.00
10.37
-0.50
-1.00
0.29
1.28039
1.28286
1.28534
1.28781
Time (s)
1.29028
1.29276
2. Calculate the change in momentum:
 In the graph created by the photo gate identify the times when the light was blocked by
the glider flag (see below)
Dual-Range Force Sensor N (+/-50) vs Time
5.50
50.00
5.00
45.00
4.50
4.00
3.50
40.00
35.00
3.00
30.00
2.50
2.00
1.50
25.00
20.00
1.00
15.00
0.50
0.00
10.00
-0.50
5.00
-1.00
0.9
1
1.1
1.2
1.3
Time (s)
1.4
1.5
1.6
1.7
1.8
 Use cursors to find dt1 the first time interval during which the light was blocked by the
glider flag. Record dt1 .
 Repeat the above step to measure dt2 the second time interval when the light was
blocked. Record dt2 .
 Use the length of the glider flag, x , and the time intervals dt1,dt2 to calculate the
velocities of the trolley before and after the impulse:
v1 
x
dt1
v2  
x
dt 2
Note that as velocity is a vector a negative sign for v2 indicates opposite direction to v1.
 Multiply the velocities by the mass m to calculate the momentum before and after the
impulse:
p1  mv1
Phil Jones
p2  mv 2
The Logical Interface
www.logint.com.au
 Calculate the difference in momentum (remember momentum is a vector):
 Record this value.
p  p 2  p1
Discussion:
Compare the impulse to the change in momentum
1. Is the change in momentum equal to the impulse?
2. Would the impulse be different if the mass was of the glider was changed? Explain your
answer.
3. Discuss any sources of error that may have affected your results.
Conclusion:
Write your own conclusion ensuring that it relates to the aim as stated above.
Phil Jones
The Logical Interface
www.logint.com.au