Experiment 2: Collisions

This report explores the interrelation between force, energy, and momentum in collisions. It discusses the conservation of momentum and energy in elastic and inelastic collisions using PASCO software and carts on a track. The experiment involves measuring velocities, energy, and momentum before and after collisions. The results show that momentum and energy are conserved in elastic collisions, but not in inelastic collisions.

Experiment 2: Collisions
Figure 1: Carts on a track.
2- Report
1. Introduction
Force, energy and momentum are directly related. It is important
therefore to investigate the interrelation between these three factors. The
daily activities involve interactions of these three elements [1]. Moving
objects have factors of the force, energy and momentum when they
interact with other objects. For any object to move, force must be applied.
When they move a distance, energy is generated [2]. Since the objects
have mass and move at certain velocity, the objects may collide with
others and therefore able to generate momentum. Momentum is defined
as a product of an object mass and velocity generated at a certain time
leading to change in direction of a mass. Collisions have each day. The
conservation of momentum is understood when knowledge is momentum

is understood [3]. Energy is the product between force and distance.
Energy is simply defined as the ability to do work. Force on the other hand
is defined as the pull or push of an object which has mass leading to
change in its velocity. The momentum, energy and force investigation
using PASCO software and carts on a track is done where measure of the
two factor under elastic and inelastic situation is done. Values before
collisions and those after collisions are recorded and compared to verify
the momentum conservation [4]. The experiment also helps to understand
how energy is only conserved in elastic collision situations. The velocities
of the carts are recorded since in order for collisions to happen, force
must be applied to generate the velocity required [10]. In the analysis, a
graph of velocity and time are obtained to show when the collisions do
happen.
2. Methodology
In this experiment, the two major equipment used include PASCO software
and carts on a track. Both carts have a wireless sensor which are used to
measure position, velocity, acceleration, the force and rotation. The
experiment involves measuring of velocities, energy and momentum
during the elastic and inelastic conditions [11]. The equipment includes
two carts (Blue and Red in color) with springs, force sensor, motion
sensor, accelerator sensor and wireless airlink. In addition, a dynamic
track with End-stop lab jack, meter stick and computer which has the
signal interface and PASCO Capstone are needed for the experiment. A
metal track where the carts move is set up where the tracks may be of

different lengths such as 0.3m and the plastic track. the accessories to the
tracks area added.
During the data collection, the cart was placed below the motion sensor.
The spring loaded bumper was set pointing downhill away from the
motion sensor. After the cart is released, the record button is pressed
instantly to start tracking the motion of the cart. Clicking on each graph
was done and then scaling to fit icon to make the data readable. A key
challenge which may be experienced during the experiment is the
movement of the hand holding the sensor may start detecting the motion
of the hand instead of the cart. One of the challenges which may be
experienced when performing this experiment is lack of proper
measurement of the distance [8]. This may arise from failure to install
properly the yellow banded plug into channels 1.
3. Analysis
Component A:
For the component A, the mass of the different carts was measures. The
experiment was used to measure the acceleration of the different carts.
From the Newton’s second law of motion, the following equation was used
to derive the force for the experiment and test for constant force [5].
Acceleration was used to test the constant force.
F= Ma
Mass of Cart 1= 0.5 kg
Try Acceleration (m/s2)
1 1.51

2 2.60
3 2.40
Using distance of 30cm, the time for accelerations is;
TRY 1, Acceleration= distance/time2
1.51 = 0.3/t2
T = root of (0.3/1.51) = 0.445s
TRY 2,
2.6 = 0.3/t2
T = root of (0.3/2.6) = 0.340s
TRY 3,
2.4 = 0.3/t2
T = root of (0.3/2.4) = 0.354s
0.445 0.354 0.34
0
0.5
1
1.5
2
2.5
3
Accelaration Vs Time Graph
The results show that the force in a mass is related to the acceleration
offered. As the acceleration increases the force increases since the mass
is constant. To stop a high accelerating mass, higher force is needed and
this is what Newton’s second law of motion stated by F=ma.

Component B:
Cart Mass VI (m/s) VF (m/s)
BLUE 0.5 0.46 0
RED 0.5 0 0.46
Calculating the momentum before collision
Momentum = m*v
For the blue cart
momentum = 0.5*0.46= 0.23 kg m/s
For the red cart
momentum = 0.5*0= 0 kg m/s
Total momentum before collision= sum off momentum for the carts
0 + 0.23 =0.23 kg m/s
Calculating the momentum after collision
For the blue cart
momentum = 0.5*0= 0 kg m/s
For the red cart
momentum = 0.5*0.46= 0.23 kg m/s
Total momentum after collision= sum off momentum for the carts
0 + 0.23 =0.23 kg m/s
Calculating the energy before collision
Energy = 1/2 *m*v2
For the blue cart
Energy = 1/2 *0.5*0.462= 0.1058J
For the red cart
Energy = 1/2 *0.5*0= 0 J
Total energy before collision= sum off momentum for the carts

0.1058 + 0 =0.1058J
Calculating the energy after collision
Energy = 1/2 *m*v2 [7]
For the blue cart
Energy = 1/2 *0.5*0= 0
For the red cart
Energy = 1/2 *0.5*0.462= 0.1058
Total energy after collision= sum off momentum for the carts
0 +0.1058 =0.1058J
Total energy vs time graph
 Include a graph of total energy vs time and total momentum
vs time. (this graph cannot be plotted since there are no
different variables for the momentum and energy)
The conservation of momentum and energy before and after the collision
is conserved [9]. This is because the same momentum and energy factors
are seen from the situation before collision and even after collision
Component C:
Cart Mass VI (m/s) VF (m/s)
BLUE 0.25 0.30 -0.30
RED 0.25 0.13 -0.24
Calculating momentum before collision,
For blue cart,
Momentum = m*v
= 0.25*0.30 = 0.075 kg m/s
For red cart,

Momentum = m*v [6]
= 0.25*0.13 =-0.0325 kg m/s
Total momentum before collision= sum off momentum for the carts
= 0.075+-0.0325= 0.0425kg m/s
Calculating momentum after collision,
For blue cart,
Momentum = m*v
= 0.25*0.30 = 0.075 kg m/s
For red cart,
Momentum = m*v
= 0.25*-0.24 =-0.06 kg m/s
Total momentum before collision= sum off momentum for the carts
= 0.075+-0.06= 0.015 kg m/s
Calculating the energy,
Energy = ½mv2 + ½mv2
Calculating energy before collision,
For blue cart,
Energy = ½mv2
= ½ *0.25*0.302 = 0.01125 J
For red cart,
energy = ½mv2
= ½ *0.25*-0.132 =0.0021125 j
Total energy before collision= sum of energy for the carts
= 0.01125+0.0021125= 0.0133625J
Calculating energy after collision,

For blue cart,
energy = ½mv2
= ½ *0.25*-0.302 = 0.01125 J
For red cart,
energy = ½mv2
= ½ *0.25*-0.242 =0.0072 j
Total energy after collision= sum of energy for the carts
= 0.01125+0.0072= 0.01845J
The momentum in this case is able to change from 0.075 kg m/s before
collision to 0.015 kg m/s after collision. This shows a loss of momentum,
which may be attributed to changes in velocity and direction of movement
of the carts. On the other hand, the total energy changes from 0.0133625J
to 0.01845J before and after collision respectively. the energy is able to
increase as the momentum is reducing. These two shows that both
momentum and energy are not conserved.
 Include a graph of total momentum vs time. (this graph cannot be
plotted since there are no different variables for the momentum)
Component D: INELASTIC
Cart Mass VI (m/s) VF (m/s)
BLUE 0.25 0.49 0.25
RED 0.25 0 0.25
The impulse in each cart is calculated as;
Impulse = Momentum Change
F • t = mass • Delta v
For blue cart,

Impulse F = m*vi- m*vf
= 0.25*0.49-0.25*0.25 = 0.06 kg.m/s
For red cart,
Impulse F = m*vi- m*vf
= 0.25*0-0.25*0.25 = -0.0625 kg.m/s
• Include a graph of momentum vs time for each cart. (this graph cannot
be plotted since there are no different variables for the momentum)
The inelastic collision does not have the energy or impulse conservation
due to the factors such as friction [12]. This can be seen in the result of
the impulse from the two carts, which are 0.06 kg.m/s and -0.0625 kg.m/s
for the blue and red cats respectively. energy is usually experienced in
these types of collisions.
General Analysis
The experiment accuracy is determined by proper reading of the factors.
The frictional force is able to hinder the movement of the carts [2], [12].
This is overcome by providing a well riding platform. High friction will
affect the decision on the conservation of both energy and momentum.
4. Conclusion
The experiment was meant to test the conservation of the Force, energy
and momentum under different situations. The types of interactions which
bodies experience are able to determine whether the conservation of
energy will be experienced or not. In most cases, the elastic situations
were able to prove that conservation of energy and momentum is

achieved. Nevertheless, on the other hand, factors such as frictional
forces in inelastic interactions are able to affecter the energy
conservation. This is seen where the initial energy before the interaction is
different from the final energy after interaction. Providing frictionless free
situation is ideal to be able to test the conservation of energy. In addition,
tracking of time factor is important to helps in the definition of the results
which are time related.
References
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