PHYS204 – Physics for Scientists and Engineers I
Lab Manual V2.0
Experiment 5:
Total Mechanical Energy, Linear Momentum, and
Kinetic and Potential Energy
(Measuring the forces of a bouncing object)
, Experiment 5: Dropping and Bouncing a Ball
INTRODUCTION
The purpose of this lab is to investigate the mechanics of a ball while bouncing and while in free-fall,
while analyzing its potential, kinetic, and mechanical energy.
As a ball bounces, it has two types of energy: kinetic and potential. Upon lifting the ball up to a certain
height, it gains potential energy, equal to the gravitation force on the ball and due to the work done to
get the ball to that height. Upon being let go, this gravitational potential energy is converted to kinetic
energy as the ball descends under the influence of the gravitational force. While the ball is in this free-
fall, this equation below describes how potential and kinetic energy are related:
1
⃑2
E (total mechanical energy) = U (potential) + K (kinetic) = mg⃑y + mv
2
The ball is modelled as a particle in equilibrium moving at a constant velocity at this point. The
gravitational potential energy is represented as:
Ug = mg⃑y (Joules)
Because energy is not lost due to conservation of energy principles, we can model the kinetic and
potential energy in this system as:
K i + Ui = K f + Uf
1 1
(mg⃑y)1 + ( mv ⃑ 2 ) = (mg⃑y)2 + ( mv
⃑ 2)
2 1 2 2
During the collision with the ground, a fraction of this kinetic energy is converted into potential energy,
and some is lost through other forms of energy, such as sound waves, compression of the ball (and the
air inside), and heat. Some kinetic energy is also absorbed by the floor – the harder the floor, the less
that is lost.
After a collision, the upward movement of the ball can be described with this equation, which is used to
describe a particle under constant gravitational acceleration:
1
y2 − y1 = v1 t − gt 2
2
Even as the ball is travelling up, it is still under the influence of the gravitation force, −𝑔. Because the
vertical height of the ball’s rebound will continually decrease until it comes to a stop, the potential
energy will also decrease with each bounce because it is dependent on height. In addition, the kinetic
energy will also continually decrease with each bounce because it is dependent on velocity.
Because both potential and kinetic energy are lost, we know that the collision is not a perfectly elastic
collision because each subsequent height obtained is less than the previous.
Another concept that will be discussed in this experiment will be linear momentum, a vector quantity.
Impulse is equal to the change in momentum of the ball.
m
⃑ = mv
p ⃑ (kg⁄ )
s
I = ∆p⃑ =p ⃑f−p ⃑ i = mv
⃑ f − mv⃑ i = m(v
⃑f−v⃑ i)
Lab Manual V2.0
Experiment 5:
Total Mechanical Energy, Linear Momentum, and
Kinetic and Potential Energy
(Measuring the forces of a bouncing object)
, Experiment 5: Dropping and Bouncing a Ball
INTRODUCTION
The purpose of this lab is to investigate the mechanics of a ball while bouncing and while in free-fall,
while analyzing its potential, kinetic, and mechanical energy.
As a ball bounces, it has two types of energy: kinetic and potential. Upon lifting the ball up to a certain
height, it gains potential energy, equal to the gravitation force on the ball and due to the work done to
get the ball to that height. Upon being let go, this gravitational potential energy is converted to kinetic
energy as the ball descends under the influence of the gravitational force. While the ball is in this free-
fall, this equation below describes how potential and kinetic energy are related:
1
⃑2
E (total mechanical energy) = U (potential) + K (kinetic) = mg⃑y + mv
2
The ball is modelled as a particle in equilibrium moving at a constant velocity at this point. The
gravitational potential energy is represented as:
Ug = mg⃑y (Joules)
Because energy is not lost due to conservation of energy principles, we can model the kinetic and
potential energy in this system as:
K i + Ui = K f + Uf
1 1
(mg⃑y)1 + ( mv ⃑ 2 ) = (mg⃑y)2 + ( mv
⃑ 2)
2 1 2 2
During the collision with the ground, a fraction of this kinetic energy is converted into potential energy,
and some is lost through other forms of energy, such as sound waves, compression of the ball (and the
air inside), and heat. Some kinetic energy is also absorbed by the floor – the harder the floor, the less
that is lost.
After a collision, the upward movement of the ball can be described with this equation, which is used to
describe a particle under constant gravitational acceleration:
1
y2 − y1 = v1 t − gt 2
2
Even as the ball is travelling up, it is still under the influence of the gravitation force, −𝑔. Because the
vertical height of the ball’s rebound will continually decrease until it comes to a stop, the potential
energy will also decrease with each bounce because it is dependent on height. In addition, the kinetic
energy will also continually decrease with each bounce because it is dependent on velocity.
Because both potential and kinetic energy are lost, we know that the collision is not a perfectly elastic
collision because each subsequent height obtained is less than the previous.
Another concept that will be discussed in this experiment will be linear momentum, a vector quantity.
Impulse is equal to the change in momentum of the ball.
m
⃑ = mv
p ⃑ (kg⁄ )
s
I = ∆p⃑ =p ⃑f−p ⃑ i = mv
⃑ f − mv⃑ i = m(v
⃑f−v⃑ i)
