PHY101
Experiment
8
Collisions
In this experiment, you will try to verify the Law of Conservation of Linear Momentum using a collision
between two cars on the air track. Here are the important concepts to understand:
A. THE LINEAR MOMENTUM P for a mass m is defined to be the product of the mass m and the velocity
v, i.e., P = mv. P is a vector quantity and its MKS unit is kg m/s. A cart moving to the right on the air track
is considered to have a positive momentum.
B. AN ELASTIC COLLISION between two objects is defined as a collision where the mechanical energy of
the system is conserved, i.e., the energy associated with the motion of the carts is not transformed into other
forms of energy. In this experiment such a collision is produced by placing a spring between the two
colliding carts.
C. AN INELASTIC COLLISION is produced when some of the mechanical energy of the carts is
transformed into other forms of energy, e.g., heat, noise etc. An inelastic collision is produced by using two
carts that stick together after the collision. Such a collision is known as a perfectly inelastic collision. Real
collisions when the objects neither conserve their mechanical energy, nor stick to each other after the
collision lie somewhere between the above two extreme cases.
The Law of Conservation of Linear Momentum applies to ALL COLLISIONS. The purpose of this experiment
is to demonstrate this fact.
The conservation statement applies to the Total Momentum of the System P = P1 + P2 where P1 = momentum
of the cart #1 and P2 = momentum of cart #2. Formally the conservation law states that:
In the absence of external forces, the total momentum of a system remains constant. (Total momentum remains
the same before and after the collision.) The force between the two carts at the instant of collision is considered
to be an internal force.
More specifically,
 An internal force is one that acts between two parts of the same system. Example: The force of collision
between two carts. Here the system is considered to be the two carts taken together. As one cart pushes on
the other the reaction force pushes back on the other cart.
 An external force is a force between one or more parts of a given system and an external object. Example:
Friction between carts (the system) and the air track (External).
PRELIMINARY QUESTIONS
For the system of a cart plus a small mass hanging in the air, as in the experiment on Newton’s 2nd Law, draw
all the forces on the system of two masses and identify which ones are internal and which ones may be
considered to be external for that experiment. Do this work in a separate page to present in your report.
Note: For each experiment, the internal and external force assignments change. It depends on what we define to
be the system in each case.
1
Compute the momenta for each of the following particles and compute the total momentum of the three-mass
system. Remember that momentum is a vector, just like velocity, i.e., direction is important and is represented
by a sign (+, –) when in 1-d:
m1 = 50 g
|v1| = 150 cm/s
m2 = 100 g
|v2| = 200 cm/s
m3 = 1 kg
|v3| = 10 cm/s
Final Analysis Table
Type of collision
Ptot before
Ptot after
% diff
Ktot before
Ktot After
% diff
Elastic Collision
Equal Masses
Inelastic Collision
Equal Masses
Elastic Collisions
Unequal Masses
Heavy impacts light
Elastic Collisions
Unequal Masses
Light impacts heavy
REPORT DUE IN 1 WEEK
Submit a lab REPORT. You do not need to propagate errors this time, but you will need to discuss the sources
of errors and estimate them in the conclusions.
You may attach the “Data Tables” as they are in pages 3, 4, 5, 6, to your report. Choose only the best trial in
each type of collision to complete the final Analysis Table above.
In the Conclusion Section, answer the following:
1) What was your initial expectation: Ptot before would be larger or smaller than Ptot after? Explain.
2) What was/were the collision(s) with the largest % difference(s)? Suggest an explanation why.
2
Elastic Collision of Two Carts of Equal Mass
Cart 1
M1 =
Cart 2
M2 =
± 0.1 g
± 0.1 g
Leff of Cart 1 through Sensor 1 =
Leff of Cart 2 through Sensor 1 =
± 0.1 cm
± 0.1 cm
Cart 1
∆t
𝑝⃗1
Before
𝑣⃗1
Cart 2
K1
∆t
𝑣⃗2
𝑝⃗2
K2
–
0
0
0
–
0
0
0
–
0
0
0
𝑝⃗2
K2
Cart 1
∆t
𝑝⃗1
𝑣⃗2
After
𝑣⃗1
Cart 2
∆t
K1
Before
𝑝⃗1 + 𝑝⃗2
After
𝑝⃗1 + 𝑝⃗2
Before
K1+K2
% diff
3
After
K1+K2
% diff
Inelastic Collision of Two Carts of Equal Mass
Cart 1
M1 =
Cart 2
M2 =
± 0.1 g
± 0.1 g
Leff of Cart 1 through Sensor 1 =
± 0.1 cm
Leff of Cart 1 through Sensor 2 =
Leff of Cart 2 through Sensor 2 =
± 0.1 cm
± 0.1 cm
Cart 1
∆t
𝑝⃗1
K1
Before
𝑣⃗1
Cart 2
𝐿𝑒𝑓𝑓 1+2
𝑣⃗1 =
∆𝑡1+2
Cart 1
𝑝⃗1
𝑣⃗2
𝑝⃗2
K2
–
0
0
0
–
0
0
0
–
0
0
0
Cart 2
𝑝⃗2
K2
𝑣⃗2 = 𝑣⃗1
K1
After
∆t1+2
∆t
Before
𝑝⃗1 + 𝑝⃗2
After
𝑝⃗1 + 𝑝⃗2
Before
K1+K2
% diff
4
After
K1+K2
% diff
Elastic Collision of Two Carts of Unequal Mass – heavy impacts light
Cart 1
M1 =
Cart 2
M2 =
± 0.1 g
± 0.1 g
Leff of Cart 1 through Sensor 1 =
± 0.1 cm
Leff of Cart 1 through Sensor 2 =
Leff of Cart 2 through Sensor 2 =
± 0.1 cm
± 0.1 cm
Cart 1
∆t
𝑝⃗1
K1
Before
𝑣⃗1
Cart 2
∆t
𝑣⃗2
𝑝⃗2
K2
–
0
0
0
–
0
0
0
–
0
0
0
𝑝⃗2
K2
Cart 1
∆t
𝑝⃗1
𝑣⃗2
After
𝑣⃗1
Cart 2
∆t
K1
Before
𝑝⃗1 + 𝑝⃗2
After
𝑝⃗1 + 𝑝⃗2
Before
K1+K2
% diff
5
After
K1+K2
% diff
Elastic Collision of Two Carts of Unequal Mass – light impacts heavy
Cart 1
M1 =
Cart 2
M2 =
± 0.1 g
± 0.1 g
Leff of Cart 1 through Sensor 1 =
± 0.1 cm
Leff of Cart 2 through Sensor 2 =
± 0.1 cm
Cart 1
∆t
𝑝⃗1
K1
Before
𝑣⃗1
Cart 2
∆t
𝑣⃗2
𝑝⃗2
K2
–
0
0
0
–
0
0
0
–
0
0
0
𝑝⃗2
K2
Cart 1
∆t
𝑝⃗1
𝑣⃗2
After
𝑣⃗1
Cart 2
∆t
K1
Before
𝑝⃗1 + 𝑝⃗2
After
𝑝⃗1 + 𝑝⃗2
Before
K1+K2
% diff
6
After
K1+K2
% diff