Conservation of Momentum

The purpose of this activity is to investigate the law of conservation of momentum through the collision of two carts.

Theory

Collisions can take on many different forms, and can involve automobiles, locomotives, shopping carts, or even two people. The force of the impact when the two objects collide depends not only on their velocities but also their respective masses (weight), and you can calculate the momentum of an object by multiplying its mass by its velocity.

Despite the variables involved, one principle always holds true – if external forces such as friction are ignored, the sum of the momenta of two objects prior to collision is the same as the sum of the momenta of the objects after collision. This is the principle known as the “conservation of momentum.” This principle is an excellent tool for understanding the dynamics of collisions.

The following expresses conservation of momentum in the case of a stationary cart being struck by another cart, after which the two carts adhere to each other and continue in motion together.

m1v1 = (m1 + m2)v2

m1(kg) : Mass of Cart 1

m2(kg) : Mass of Cart 2

v1(m/s) : Velocity of Cart 1 Before Collision

v2(m/s) : Velocity of Two Carts After Collision

This means that when the two carts are of identical mass, the combined velocity of the two carts after collision is one half that of the velocity of Cart 1 before the collision.

The above expression can be used to obtain the post-collision velocity of two carts (while they

adhere to each other) of different masses.

2-3-1

English

Activity:tivity: SetupSetup

￿ Equipment

Two carts of identical mass

String

Pulley with a bracket to secure it

Velcro￿

500g weight

Cushion

Distance Measurement Setup (EA-200, graphic scientific calculator, data communication cable, optional EA-2*1)

￿Preparing the Carts

u Measure the masses of Cart 1 and Cart 2.

uAffix Velcro￿ to the impact surfaces of Cart 1 and Cart 2.

uUse tape to securely affix the string to the center of the front end (the same end where the Velcro￿ is affixed) of Cart 1.

1 Back of Cart 1

2String

3Velcro￿

￿Setting Up

uAlign the EA-2, Cart 1, Cart 2 and the pulley in a straight line.

uRun the string under Cart 2 and place it onto the pulley. Attach the weight to the end of the string.

u Support the weight with your hand so it does not pull Cart 1.

1 Cart 1

9 Distance: 50cm

*1

2 Cart 2

0 Height of weight

 

3 Pulley

from floor: 30cm

 

 

 

4 500g weight

! Desk

 

5 String

@ Floor

 

 

 

6 Cushions

# Velcro￿

 

7 EA-2 (SONIC)

$ EA-200

 

8 Allow 60cm

 

 

between EA-2

 

 

and Cart 1.

 

 

 

 

 

*1 When using the EA-200 in combination with the optional ‘‘Motion Sensor (EA-2) ”, be sure to

power the EA-200 using its bundled AC adaptor (AD-A60024).

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