One Dimensional Conservation of Momentum and Energy

**One** **Dimensional** **Conservation** **of** **Momentum** **and** **Energy**

Purpose

1. Study the conservation **of** momentum **and** energy in one dimension by examining the

motion **of** colliding carts on a track.

2. Determine velocity for one **of** two carts after their collision

Introduction

The method employed in this experiment is much like any which use the carts **and** track.

Theory

1. **Momentum** **and** energy

For bodies travelling in one dimension, position **and** velocity can be simply specified;

position will be a distance from the origin, **and** velocity will be either positive or negative

based on the direction **of** travel. (For instance, an object travelling to the right may be

considered to have a positive velocity, while one travelling to the left will have a negative

velocity.) When two objects moving in one dimension collide, the following equations hold:

Initial momenturm=

P = mv + m v

i

1 1i

2 2i

(1)

2 1

Initial energe = E = m v + m v

1 1i

2

2 2

1 2

1 2 i

Final momenturm = P = m v + m v

f

1 1 f

2 2 f

2 1

Final energe = E = m v + m v

f

1 f

2

2 2

1 2

1 2 f

(2)

(3)

(4)

Since velocities can be positive or negative, this means that in the above equations,

momentum can be positive or negative, while energy must always be positive (unless it is

zero, in which case there is no motion.)

2. Elastic collision

For any collision, momentum should be conserved. However, energy will only be

conserved if a collision is elastic. When two bodies collide, an elastic collision doesn’t

lose energy because the mechanic energy doesn’t convert into heat while an inelastic

collision does lose energy. To have an elastic collision, the carts are equipped with

magnets. Once they are collided, their bodies don’t touch each other. It enables the

collision elastic.

3.Dependent measurement

This experiment will require calculations with repeated dependent measurements. For

repeated dependent measurements please see Experiment 4.

Apparatus

1. two carts with magnets

2. a track

3. a computer connected with sensors

4. several iron blocks

Figure 1 Two carts collide when m 1 =m 2

Figure 2 Two carts collide when m 2 >>m 1

Procedures

1. Make sure the track is level before you begin this experiment.

2. Without recording data, try a sample collision by having one cart (m 1 ) collide with the

other (m 2 =m 1 ) which is initially at rest, as shown in Figure 1. Then do the same thing the

other way around, i.e. the cart which was previously at rest will now be the one initially

moving.

(Q1: Is there any obvious reason for choosing which cart to have at rest so that your data

will be easier to analyze If so, explain.)

3. As shown in Figure 2, adding three more magnets on a cart (m 2 ) so that m 1