The Cart and the Brick Activity

Begin Activity

View a Sample Analysis

In this activity, you will analyze a collision in order to
determine the total momentum of a system before and after the
collision. Your goal is to gather evidence that supports the law of
conservation of momentum. The collision involves the collision between
a stationary brick that is dropped upon a moving cart. The brick
lands upon the cart and travels at the same speed as the cart after the
collision. A ticker tape is attached to the cart and pulled along with
the cart through a ticker tape timer. Ticks (dots) are placed upon the
tape every 1/60-th of a second, leaving a trace of the cart's position
over the course of time. Analysis of the ticker tape allows one to
determine the velocity of the cart before and after the collision.

Sample Analysis

Given:The ticks (dots) are left by the cart every 1/60-th of a
second. The spacing between every 6th dot (for example, from the 1st
dot to the 7th dot) is equal to the distance traveled in a time of 0.10
seconds. This information can be used to determine the before- and
after-collision velocities.

slow

Pre-Collision Speed:

3.0

Mass of Brick (kg):

= 1.0 cm

The goal is to determine the total system momentum before and
after the collision. The masses are known. So the first step is to
determine the velocities before and after the collision.

Continue

Mass of Cart (kg):

SCALE:

4.0

To determine the before-collision velocity, one must use the fact
that the ticks on the ticker tape were left every 1/60-th of a second.
For this reason, the spacing before every sixth tick is equivalent to
the distance traveled in 6/60-ths second or 0.10 seconds. The work is
shown below the graphic.

The distance circled on the left represents the distance traveled
in 0.30 seconds - a time equivalent to 18 spaces. Using the scaled
centimeter, this distance is equivalent to approximately 10.7 cm. So
the before-collision velocity is 10.7 cm/0.30 s = 35.6666… cm/s = 35.7
cm/s. The before-collision momentum of the cart is (4.0
kg)•(35.6666… cm/s) = 142.6666 kg•cm/s = 143 kg•cm/s.

The distance circled on the right represents the distance traveled
in 0.30 seconds - a time equivalent to 18 spaces. Using the scaled
centimeter, this distance is equivalent to approximately 6.0 cm. So the
after-collision velocity of the cart and the brick is 6.0 cm/0.30 s =
20.0 cm/s. The after-collision momentum of the cart and brick
is (7.0 kg)•(20.0 cm/s) = 140 kg•cm/s.

Exit Sample Analysis

So for this sample collision, it has been shown that the 4.0-kg
cart has a before-collision momentum of 143 kg•cm/s. Since the cart is
the only object moving before the collision, the total system momentum
is 143 kg•cm/s.
After the collision, it has been shown that the combination of the
4.0-kg cart with the 3.0-kg brick on top of it has a momentum of
140 kg•cm/s. This is the total system momentum after the collision.
One would expect there to be small amounts of error inherent in the
process of measuring the velocity of the moving cart. The distances
traveled during the 0.30 seconds were best estimates and thus subject
to small amounts of error. Within a reasonable margin of error - two
significant digits - one can confidently say that the total system
momentum is the same before the collision as it is after the collision.
For this reason, one can conclude that momentum is conserved in this
collision.

medium

fast

slow

Select Experimental Conditions

You have a choice of trials that you can run. The trials differ
from one another in terms of the mass of the cart, the mass of the
brick, and the pre-collision speed of the cart. Click on one of the set
of conditions below to run the trial. Click on the More Conditions
button for more possibilities.

More Conditions

2.0-kgcart

3.0-kgcart

1.5-kg brick

4.0-kgcart

2.5-kg brick

Previous Conditions

You have a choice of trials that you can run. The trials differ
from one another in terms of the mass of the cart, the mass of the
brick, and the pre-collision speed of the cart. Click on one of the set
of conditions below to run the trial. Click on the Previous Conditions
button for other possibilities.

Trial A1 Conditions

Analyze the ticker tape diagram (dot diagram) left by the cart to
determine the pre-collision and post-collision velocities. Combine this
velocity information with the mass values to determine the total
momentum of the system before and after the collision. Is momentum
conserved by the system?

2.0

Given:The ticks (dots) are left by the cart every 1/60-th of a
second. So every 10 dots is equal to a time of 0.10 seconds.The large
divisions on the distance scale below the ticker tape are 1.0-cm apart.

1.5

Repeat Animation

Change Conditions

Analyze Data

Given:The ticks (dots) are left by the cart every 1/60-th of a
second. So the spacing between every 6th dot (for example, from the 1st
dot to the 7th dot) is equal to the distance traveled in a time of 0.10
seconds.

Analyze the ticker tape diagram (dot diagram) left by the cart to
determine the pre-collision and post-collision velocities. Combine this
velocity information with the mass values to determine the total
momentum of the system before and after the collision. Can you gather
such data and present it as evidence to support the principle that
momentum is conserved by the system?

medium

Trial A2 Conditions

Analyze the ticker tape diagram (dot diagram) left by the cart to
determine the pre-collision and post-collision velocities. Combine this
velocity information with the mass values to determine the total
momentum of the system before and after the collision. Can
you gather such data and present it as evidence to support the
principle that momentum is conserved by the system?

fast

Trial A3 Conditions

Trial B1 Conditions

Trial B2 Conditions

Trial B3 Conditions

Fast

Trial C2 Conditions

Trial C1 Conditions

Trial C2 Conditions

Trial C3 Conditions

2.5

Trial D1 Conditions

Trial D2 Conditions

Trial D3 Conditions

Trial E1 Conditions

Trial E2 Conditions

Trial E3 Conditions

Trial F1 Conditions

Trial F2 Conditions

Trial F3 Conditions