Physics
Motion and Forces
Sensors:
Loggers:
Light gates
Any EASYSENSE
Logging time: Timing, Speed /
Velocity at A then B
28 Conservation of linear momentum using Light
gates to measure velocity
Read
When two vehicles collide, momentum is exchanged between them. Sometimes the vehicles will bounce off
one another like colliding protons in a nuclear event, and in other cases the vehicles will stick together after
the collision as in galaxies colliding or sometimes in road traffic accidents.
You are to compare the total momentum before a collision with the total momentum after the collision to find
out whether momentum is conserved (remains the same) during a collision.
You will use low friction carts, to reduce the external forces acting during the collision.
You will investigate two types of collision:
1. Elastics collisions using repelling magnets or a spring so the carts bounce off one another.
2. Inelastic collisions using a needle sticking into a soft target, so that the carts stick together after the
collision.
Theory
Momentum = mass x velocity
P=mv
Velocity is a vector quantity, and therefore momentum is also a vector quantity. We will assume that velocities
and momenta from left to right are positive.
Consider the following elastic collision between two carts of mass m1 and m2.
Before the collision: the carts will have a velocity defined by U1 and U2.
U1
U2
m1
M2
Total Momentum = m1u1 + m2u2
NB. In the experiment cart 2 is travelling towards cart 1. Its velocity u2 will be negative.
After the collision: The carts will have a velocity defined by V1 and V2.
Motion and Forces
28 - 1 (V2)
V1
V2
m1
M2
Total Momentum = m1v1 + m2v2
In this experiment v1 will be from right to left and therefore negative.
In this experiment you are to compare the Total Momentum before and after the collision.
Consider the following inelastic collision:
Here one cart has a needle, which sticks into Blu-Tack attached to the other cart which makes them stick
together after the collision
Before the collision: Cart 1 will have a velocity defined by U1 and cart 2 will have a velocity of 0.
U1
Stationary
m1
M2
Total momentum = m1u1 + m2 x 0
= m1u1
After the collision: The carts will have a velocity V.
V
m1
M2
The carts stick together after the collision and move off with the same velocity.
Total momentum = m1v + m2v
= (m1 + m2) v
What you need
1.
2.
3.
4.
5.
6.
7.
8.
9.
An EASYSENSE logger.
2 Smart Q Light gates
Dynamics track
2 low friction dynamics carts with 120 mm single interrupt cards mounted on the top of each cart.
Compression spring or 2 magnets from the accessory kit or 2 magnadur magnets
Needle for mounting on one of the carts.
Blu-Tack or modelling clay.
Digital balance to measure the mass of the trolleys.
Elastic bands may also be used to simulate elastic collisions.
Motion and Forces
28 - 2 (V2)
3xL
The diagram shows carts fitted with magnets. If like poles of the magnets face each other then an elastic
collision will take place. If a spring is being used it should be fitted to the cart that will be pushed to the
stationary cart. The gap between the Light gates should be at least 3 times the length of the cart; this will
allow both carts to be between the Light gates at the moment of collision.
What you need to do
Elastic collisions – one cart moving
1. Assemble the apparatus as shown in the diagram above. Note how one cart is stationary between
the Light gates. There should be enough space for both carts to be between the Light gates at the
same time.
2. Attach the spring to one of the carts so that it will contact the second cart and push it away. If
necessary adjust the distance between the Light gates to compensate for the extra length created by
the spring.
3. Weigh both carts and note down their masses.
4. Arrange the collision point to be midway between the Light gates.
5. Push the cart with the spring gently towards the other cart. Find, by trial and error, the maximum
appropriate speed to push it. If the speed of the collision is too high the carts will start to jump, if the
speed is too low, friction will play too large a part.
6. Connect the first Light gate to input A and the second Light Gate 2 to input B on the logger.
7. From the EasySense software’s Home screen select Open Setup (or File, Open Setup). Open the
file Data Harvest Investigations (Edition 2) \ Setup files \ Physics_Motion and Forces_L3 V2 \ 28
Conservation of linear momentum.
8. Click on the Start icon to begin logging. Push the cart to collide with the stationary cart. Reposition
the carts for another run. Take care to not pass the carts through the Light gates as you do this.
9. Complete 3 collisions and then click on Stop.
10. Delete any unwanted data by selecting it and using Delete.
11. Double click on each Comment cell in turn and name the successive collisions 1, 2, 3, etc.
12. Save the file.
Motion and Forces
28 - 3 (V2)
Inelastic collisions
1. Replace the spring with a needle mounted on cart 1and Blu-Tack or modelling clay in a cone on cart
2, so that the carts will stick together after colliding.
2. Reweigh the carts and note down the masses.
3. Place cart 2 stationary between the Light gates and push cart 1 towards it so that they stick together.
Try a couple of times before starting to log the data. Cart 1 must have got completely through Light
gate 1 before it hits cart 2.
4. Click on Start to start logging and push cart 1 towards cart 2.
5. Repeat two more times, and then click on the Stop icon to finish logging.
6. Save the file.
Elastic collisions – both carts moving
1. Replace the mounted needle and modelling clay with a spring. Try to push the carts together and
make them collide with each other (when they are both moving). Try to get the collision between the
Light gates. You must make sure the interrupt cards have both travelled through the Light gates
before the collision starts. You may need to practice this few times.
2. If there is time available repeat the experiments using carts with different masses.
Results and analysis
Elastic collisions: Cart 1 moving and colliding with stationary cart 2
For each elastic collision fill in the following table.
Mass of cart 1 = ………..kg
Mass of cart 2 = ………..kg
Collision No.
Before the collision
Velocity u1 (m/s)
Velocity u2 (m/s)
Momentum of m1 (kgm/s)
Momentum of m2 (kgm/s)
After the collision
Velocity v1 (m/s)
Velocity v2 (m/s)
Momentum of m1 (kgm/s)
Momentum of m2 (kgm/s)
Change in momentum
(kgm/s)
Motion and Forces
28 - 4 (V2)
u1 = the velocity of cart 1 before the collision
u2 = the velocity of cart 2 before the collision
v1 = the velocity of cart 1 after the collision
v2 = the velocity of cart 2 after the collision
m1, m2 = the mass of the carts 1 and 2 respectively
Elastic collisions: Carts both moving and colliding
For each elastic collision fill in the following table.
Mass of cart 1 = ………..kg
Mass of cart 2 = ………..kg
Collision No.
Before the collision
Velocity u1 (m/s)
Velocity u2 (m/s)
Momentum of m1 (kgm/s)
Momentum of m2 (kgm/s)
Total momentum (kgm/s)
After the collision
Velocity v1 (m/s)
Velocity v2 (m/s)
Momentum of m1 (kgm/s)
Momentum of m2 (kgm/s)
Total momentum (kgm/s)
Change in momentum
(kgm/s)
Inelastic collisions: One cart colliding with another, both carts continuing, joined together
after the collision
Mass of cart 1 = ……. kg
Mass of cart 2 = ……. kg
For each inelastic collision fill in the following table.
Collision No.
Before the collision
Velocity u1 (m/s)
Momentum (kgm/s)
After the collision
Velocity v (m/s)
Momentum (kgm/s)
Change in momentum
(kgm/s)
Motion and Forces
28 - 5 (V2)
Evaluation and conclusions
Using your results answer the following questions about elastic and inelastic collisions:
•
In which of the collisions was the momentum conserved (i.e. it stayed the same before and after the
collision)?
•
Where are the sources of error in the experiment, and how do they affect the results you gained?
•
Fill in the Summary Table putting yes or no in the blank boxes.
Summary table
Elastic collision
Inelastic collision
Is momentum conserved?
Questions
On a dynamics system (or air-track) a 0.2 kg cart travelling at 0.3 ms-1, collides with a 0.3 kg vehicle
travelling in the same direction at 0.1 ms-1 the vehicles stick together. Calculate the following:
a. The initial momentum of the 0.2 kg vehicle.
b. The initial momentum of the 0.3 kg vehicle.
c.
The combined velocity of the vehicles after the collision.
Motion and Forces
28 - 6 (V2)