this lab report include the simple and most reliable technique to solve the problem for coefficient of restitution.

1. [1]
DHA SUFFA UNVERSITY KARACHI
MECHANICAL ENGINEERING DEPARTMENT
Engineering Dynamics Lab
ME-2101L
(Semester fall-2019-20)
Course instructor: Engr. Najiullah Hussaini
Open ended lab
Group members:
Muhammad Shehryar Imtiaz me181056
Sufyan Baig me181008
Abdul Rafeh me181044

2. [2]
OBJECTIVE:
Design an experiment to determine coefficient of restitution of different materials and their
combinations.
TOPIC:
The purpose of this experiment is to determine the coefficient of restitution for various balls.
THEORY:
COLLISION:
A collision is the event in which two or more bodies exert forces on each other in about a
relatively short time. Although the most common use of the word collision refers to incidents in
which two or more objects collide with great force.
ELASTIC COLLISION:
An elastic collision is a collision in which there is no net loss in kinetic energy in the system as a
result of the collision. Both momentum and kinetic energy are conserved quantities in elastic
collisions. ... They collide, bouncing off each other with no loss in speed.
INELASTIC COLLISION:
An inelastic collision is a collision in which there is a loss of kinetic energy. While momentum
of the system is conserved in an inelastic collision, kinetic energy is not. This is because some
kinetic energy had been transferred to something else.
COEFFICIENT OF RESTITUTION:
The coefficient of restitution is the ratio of speeds of a falling object, from when it hits a given
surface to when it leaves the surface. In laymen's terms, the coefficient of restitution is a measure
of bounciness. A ball is a round or spherical object that is used most often in sports and games.
Balls are made from different materials, but leather, rubber, and synthetics are the most common
in modern times.
The coefficient of restitution is found by the formula

3. [3]
𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑅𝑒𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 =
𝑠𝑝𝑒𝑒𝑑 𝑢𝑝
𝑠𝑝𝑒𝑒𝑑 𝑑𝑜𝑤𝑛
.
ENERGY CONSERVATION:
CONSERVATION OF MOMENTUM:
For a collision occurring between object 1 and object 2 in an isolated system, the total
momentum of the two objects before the collision is equal to the total momentum of the two
objects after the collision. That is, the momentum lost by object 1 is equal to the momentum
gained by object 2. The total momentum of a collection of objects (a system) is conserved - that
is, the total amount of momentum is a constant or unchanging value.
CONSERVATION OF MECHANICAL ENERGY:
If only conservative forces act, then 𝑊𝑛𝑒𝑡 = 𝑊𝑐 where 𝑊𝑐 is the total work done by all
conservative forces. Thus, 𝑊𝑐 = 𝛥𝐾𝐸.
Now, if the conservative force, such as the gravitational force or a spring force, does work, the
system loses potential energy (PE). That is, 𝑊𝑐 = −𝑃𝐸. Therefore,
𝛥𝑃𝐸 = 𝛥𝐾𝐸
𝑚𝑔ℎ =
1
2
𝑚𝑣2
This equation means that the total kinetic and potential energy is constant for any process involving
only conservative forces.
ANALYSIS:
In order to find speed we had to use the average height that we measured, and put it in the
formula
𝑣 = √(2𝑔ℎ)

4. [4]
Where v = velocity, g = 9.8m/s2, and h = average height measured.
Now to find the coefficient of restitution, this formula is used.
𝒆 =
𝑣2 − 𝑣1
𝑢2 − 𝑢1
EQUIPMENT:
Wooden board with base mounted supports. Total height of 1.2 meters. On wooden board inch
tape is stick to it to find the height.
MATERIAL:
 Wooden wall.
 Wooden base
 Rubber balls
 Inch tape
 Multiple testing material

5. [5]
PROCEDURE:
 Take the ball and hold it at a set height above the surface. (We chose a height of 92 cm
for all trials.)
 Drop the ball and record how high it bounces.
 Repeat now using different materials.
 Try using these balls at first for elastic collision
Practice golf ball
Wilson tennis ball
Rubber band ball (many rubber bands put together in ball form)
Steel ball bearing
Glass marble
OBSERVATION:
S. NO. MASS OF
MATERIAL
HEIGHT INITIAL
VELOCITY
FINAL
VELOCITY
e
1-
2-
3-
4-
5-
6-
7-

6. [6]
SOURCES OF ERROR:
 The ball didn't bounce straight up because of uneven or cracked ground, which would
have stopped the ball from reaching its peak height.
 When releasing the ball from your hand the ball rotates slightly, causing the ball to lose
some of its translational energy which in turn causes the ball to not bounce as high as it
would in a perfect world.