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Experiment on Conservation of Linear Momentum, Lab Reports of Physics

The purpose of this experiment is to reproduce a simple experiment demonstrating the Conservation of Linear Momentum.

Typology: Lab Reports

2020/2021

Uploaded on 05/11/2021

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Experiment 7 ~ Conservation of Linear Momentum
Purpose:
The purpose of this experiment is to reproduce a simple experiment demonstrating the
Conservation of Linear Momentum.
Theory:
The momentum p of an object is the product of its mass and its velocity:
p = mv
Momentum is a vector quantity, since it comes from velocity (a vector) multiplied by mass (a
scalar). The law of conservation of momentum states that the total momentum of all bodies
within an isolated system,
ptotal = p1 + p2 + .......,
is constant. That is, if the total momentum has some initial value pi, then, whatever happens
later, the final value of the total momentum pf must equal the initial value. So we can write the
law of conservation of momentum like this:
pf = pi
Conservation of momentum is usually studied in problems that involve collisions. In this
experiment, you’ll look at collisions between two gliders on an air track. You will measure the
final momentum of an initially stationary glider, struck by another glider which is initially
moving. You’ll do this experiment for two different types of collisions, elastic and inelastic.
Elastic collisions are ones where kinetic energy is conserved (the objects bounce off each other
without losing any energy). Inelastic collisions (e.g., if the objects get stuck together) do not
conserve kinetic energy. The kinetic energy of an object is defined as
where m is the object’s mass and v is its velocity. Kinetic energy is not a vector: it’s a scalar, and
its units are Joules (J).
pf3
pf4
pf5

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Experiment 7 ~ Conservation of Linear Momentum

Purpose:

The purpose of this experiment is to reproduce a simple experiment demonstrating the

Conservation of Linear Momentum.

Theory:

The momentum p of an object is the product of its mass and its velocity:

p = mv

Momentum is a vector quantity, since it comes from velocity (a vector) multiplied by mass (a

scalar). The law of conservation of momentum states that the total momentum of all bodies

within an isolated system,

p total

= p1 + p 2

is constant. That is, if the total momentum has some initial value p i

, then, whatever happens

later, the final value of the total momentum p f

must equal the initial value. So we can write the

law of conservation of momentum like this:

p f

= p i

Conservation of momentum is usually studied in problems that involve collisions. In this

experiment, you’ll look at collisions between two gliders on an air track. You will measure the

final momentum of an initially stationary glider, struck by another glider which is initially

moving. You’ll do this experiment for two different types of collisions, elastic and inelastic.

Elastic collisions are ones where kinetic energy is conserved (the objects bounce off each other

without losing any energy). Inelastic collisions (e.g., if the objects get stuck together) do not

conserve kinetic energy. The kinetic energy of an object is defined as

where m is the object’s mass and v is its velocity. Kinetic energy is not a vector: it’s a scalar, and

its units are Joules (J).

Part I: Inelastic Collisions

Equipment:

Before you begin this experiment, you have to make sure the air track is level. First, turn the air

supply on. Place a glider in the middle of the track with no initial velocity. Adjust the leveling

screws until the glider remains in its initial position, not accelerating in either direction. The

glider may oscillate slightly about its position. This movement is caused by air currents from the

air holes in the track and should be considered normal.

Figure 1 illustrates the experimental method used for observation of inelastic collisions.

Glider 2, fitted with a Velcro impact pad (to make the gliders stick together!), will be positioned

at rest between Photo gate 1 and Photo gate 2. Glider 1 will be fitted with a measurement flag

and a needle.

Experiment:

For this part of the lab you will use the laptop connected to your set up. Save the Data Studio file

to the desktop. The .ds file can be downloaded from the Physics lab site at:

http://umsl.edu/~physics/lab/mechanicslab/11-Lab7.html. Once you have the laptop on and

the sensors plugged in you can double click on the saved file to open the Data Studio program. If

you need to find it later the program can be found in the ‘Education’ folder under the programs

in the start menu. To start taking measurements, click on the run button on the upper tool bar.

The lab TA will provide more instruction. If you make a mistake with the program you can start

over by closing the program without saving and opening it again from the Desktop.

Start recording the data for the first measurement.

Give Glider 1 a push. As it passes through Photo gate 1, a time interval (the “before” time) will

be measured. The velocity and momentum of Glider 1 can be computed from time data measured

and the mass of the glider.

Once Glider 1 strikes Glider 2, the two should stick together. The resulting momentum of the

coupled Gliders 1 and 2 can be computed from their total masses and the velocity measured at

Photo gate 2 (the “after” time). Once the gliders have stuck together, you can treat them as a

single object. Since the recorder is measuring time, the velocity recorded is automatically

computed using the 2.5 cm flag width (∆x).

Do this experiment a few times, and record your data.

Figure 1

Part II: Elastic Collisions

Equipment:

Figure 2 illustrates the experimental method used for observation of elastic collisions. In

this part of the experiment, you’ll observe the momenta (plural of momentum!) of a pair of

gliders before and after an elastic collision. Keep the photo gates in the same positions as in the

first part of the experiment. Remove the Velcro pads from the gliders. Attach rubber bumpers to

Gliders 1 and 2, and then position Glider 2 at rest between Photo gate 1 and Photo gate 2. Both

Gliders 1 and 2 will be equipped with vertically positioned-measurement flags.

Experiment:

Clear the previous data runs. Make sure that Glider 2 (the one that is going to be hit) is

placed between the two photo gates. Glider 1 should be outside the photo gates (see Figure

2).The first time measurement (“time before”) will be made by giving Glider 1 a push. Push it

gently (we’ll explain why in a moment). As Glider 1 passes through Photo gate 1, a time interval

will be measured. The initial velocity, momentum and kinetic energy of Glider 1 can be

computed from the velocity measured, and from the mass of Glider 1.  Now, this is why you

want to push Glider 1 gently. You want it to hit Glider 2 so that Glider 2 will start moving, but

Glider 1 will stop moving. Think of a situation where one pool ball hits another and then stops –

but the second ball, the one that was hit, starts moving. That’s what you want to do with the

gliders. Basically you are transferring all the kinetic energy of Glider 1 to Glider 2! 

The second velocity you will measure is the velocity of Glider 2 as it passes through the second

photo gate. This is our “time after”. The momentum and kinetic energy of Glider 2 can be

computed from the velocity measured, and from the mass of Glider 2.

Figure 2

Data and Calculations:

m 1

= Kg m 2

= Kg

Equation for initial and final momentum:

(mv) (^) o=

(mv) (^) f =

Equation for initial and final kinetic energy:

KEo =

KEf =

v (m/s)

=d/t

mv (Kg m/s)

(momentum)

mv

2 (J)

(kinetic energy)

Before After Before After Before After

Part II: Elastic collisions

  1. For each run of your elastic collision experiment, calculate the percent difference between the

initial momentum and the final momentum. Does your data indicate conservation of

momentum? Is the “before” velocity of Glider 1 equal to the “after” velocity of Glider 2? Why or

why not?

  1. For run of your elastic collision experiment, calculate the percent difference between the

initial energy and the final energy. Does your data indicate conservation of energy?

  1. List some possible source of error in this part of the experiment. Are these sources of error

random or systematic?

mv (Kg m/s)

(momentum)

Before After

% difference

mv

2 (J)

(kinetic energy)

Before After

% difference