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# The Physics of Collisions

The physics part in collisions. To understand collisions you just need to know the basic laws and rules of physics.
by

## Hatza Rozga

on 20 January 2014

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#### Transcript of The Physics of Collisions

The Physics of Collisions
Momentum
Momentum is defined as mass in motion. If an mass is moving then it is said to have momentum.
Newtons Laws and Collisions
Newton's laws of motion make us understand the motion of objects.
Collision Impact on People
People are thrown around in car accidents.
Conclusion
Momentum
Momentum Equation
The Law of Conservation of Momentum
The total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision in an
isolated system.
Rebounding
Occasionally when objects collide, they bounce off each other. In rebounding, the objects direction changes from before the collision. Rebounding happens only when there will be large velocity and momentum changes.
The Law of Conservation of Kinetic Energy
In collisions where kinetic energy remains constant, we say that the kinetic energy is conserved. So the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Types of Collisions
Newton's First Law of Motion
A body will continue to be at rest or motion unless acted upon an unbalanced external force.
Newton's Second Law of Motion
F= (m)(a)
Newton's Third Law
Every action has an equal and opposite reaction.
Impulse-Momentum Change Theorem
Analysis of Physical Situations Involving Collisions and Impulses
Example Scenario
The Equation
Inelastic Collisions
Elastic Collisions
Collisions are when two or more objects apply forces on each other for a small period of time.
What are Collisions?
Momentum depends on two things. Mass and Velocity. Momentum is the product of mass and velocity. The variable for momentum is a lower case "p." The SI unit for momentum is kgm/s. "m" is the mass in kg. "v" is the velocity in m/s.
p= m x v
A object/body that has mass and is in motion is said to have momentum.
Impulse = Change in Momentum

Newtons second law of motion:
F= (m)(a)
(F)(t) = (m)(delta v)
(F)(t)
In a collision, an object experiences a force for a specific amount of time that results in a change in momentum.
A system in which the only forces that contribute to the momentum change of an individual object can be considered an
isolated system.
Initial Momentum = Final Momentum
For 2 objects.
The Physics of Collisions
Kinetic Energy is the energy of motion. It depends on 2 variables, m(mass) in kg and v(speed) in m/s. Any object whether horizontal or vertical that is in motion will have kinetic energy.
Kinetic Energy
Total K.E before collision = Total K.E after collision.
This means energy is conserved, meaning that the kinetic energy has not been changed.
Inelastic Collisions
Elastic Collisions
2 Types:
1.
2.
Inelastic collisions happen when kinetic energy isn't conserved but momentum is conserved. Most or almost all collisions are inelastic.
According to Newton's third law, when two objects collide, both objects experience equal amount of force, in the opposite direction.
Force is the product of mass times acceleration. To calculate the force of the collision we can use Newton's law, F = (m)(a).
F
m
a
Will continue to stay at rest unless someone moves it.
A pendulum could swing forever if there was no air resistance and friction.
Tennis
Mass of tennis ball = 56.7g.
Change in velocity = 68m/s
Change in time = 0.025 s
[F][t]
= [0.0567kg]
[2720m/s ]
[0.025s]
[m][delta v]
= [0.0567kg]
[68m/s]
= 4.0 kgm/s
= 4.0 kgm/s
Impulse = Change in Momentum
A ball that is 4.5kg is moving at 5.0m/s and hits a 6.0kg ball that is moving at 7.5m/s. The velocity of the ball that was 4.5kg is 2.5m/s after the collision. What is the velocity of the 6.0kg ball?
The 3 main ideas
From Newton's 1st law of motion, a body in motion will continue to be in motion unless acted upon an unbalanced external force.
So when a person hits another car that is in motion too, the drivers the people, things and the internal organs of the people, in the cars will continue moving until they bang into something that makes them to stop moving.
Warning!
Kinetic Energy
Newton's Laws of Motion
(delta v)(m)
a =2720m/s
m = 94 000 kg
v = 1504 km/hr
= 1/2 [94000kg] [1504000m/s]
= 1504000 m/s
2
= 1.06314752 x 10 J
17
K.E = 1.1 x 10 J
17
When Bigger Vehicle Hits Smaller Vehicle
Elastic collisions happen when momentum and kinetic energy are conserved.
Example: Two cars
crashing
= 3.8556kgm/s
= 3.8556kgm/s
2
2
NOTE:

when something falls down the speed increases, thus this example is not totally correct. Kinetic energy will be the greatest when the airplane is the closest to the ground.
Before Collision:
Blue car
Yellow car
Total K.E
K.E = [500kg][5m/s][5m/s]
= 6250J
2
K.E = [400kg][2m/s][2m/s]
2
= 800J
= 6250J + 800J
= 7050J
After Collision
Blue car
Yellow car
Total K.E
K.E = [500kg][3.0m/s]3.0m/s]
2
= 2250J
K.E = [400kg][4.5m/s][4.5m/s]
2
= 4050J
= 2250J + 4050J
= 6300J
Before Collision
After Collision
Blue Car
Yellow Car
Blue Car
Yellow Car
Total p:
Total p:
p = mv
= [500kg]
[5m/s]
= 2500kgm/s
= 2500kgm/s + 800kgm/s
=3300kgm/s
p = mv
= [400kg]
[2m/s]
= 800kgm/s
p = mv
p = mv
= [500kg]
[3.0m/s]
= [400kg]
[4.5m/s]
= 1500kgm/s + 1800kgm/s
= 1500kgm/s
= 1800kgm/s
=3300kgm/s
Without Sig Figs
Without Sig Figs
Without Sig Figs
Without Sig Figs
Eg. Rebounding
The unit for Force is Newtons : N
Since the force is equal
(from Newton's third law of motion)
the acceleration is not equal, because the masses are different
(from Newton's second law of motion.)
The acceleration = F/m. Thus the bigger the mass the smaller the acceleration. Both the vehicles will experience the same force and for the same amount of time so the impulses and change in momentum are the same. When the change in momentum is the same, the change in velocity will be greater for the less heavier vehicle. So when the change in velocity is also greater, and the change in kinetic energy will also be greater, thus the work done on the driver of the smaller vehicle will also be greater. The bigger vehicle is harder to stop because it's mass is greater than the smaller vehicle. The smaller car will have more damage due to the larger mass of the bigger car. So when you look at it from any way it is safer to to ride in a bigger vehicle that has a larger mass. So anything that has more mass, is at a greater advantage.
Force =
272000 N
Mass of bigger vehicle =
2700kg
Mass of smaller vehicle =
500kg
a of smaller vehicle
a of bigger vehicle
a = F/m
a = 272000 N/500kg
a = 500m/s
2
a = F/m
a = 272000 N/2700kg
a = 1.0 x 10 m/s
2
2
The acceleration of the smaller vehicle is greater.
Eg. two cars crashing
By : Srija
Thank You. The End.
Work Energy Principle
Net Work =
Work done on the object
Final
Kinetic energy
Initial
Kinetic energy
The
net work
is the change in kinetic energy. So the more change in velocity, the more change in kinetic energy, and the more change in kinetic energy, the more work done on an the object.
Change in Momentum =
14144000kgm/s
Mass of bigger vehicle =
2700kg
Mass of smaller vehicle =
500kg
delta v of smaller vehicle
delta v of bigger vehicle
delta v = delta p/m
delta v = delta p/m
= 14144000kgm/s /500kg
= 14144000kgm/s /2700kg
= 5200m/s
= 30,000m/s
The change in velocity is greater for the smaller vehicle.
ball1 + ball2 = ball1 + ball2
Initial
Final
[4.5kg][5.0m/s] + [6.0kg][7.5m/s] = [4.5kg][2.5m/s] + [6.0kg][v]
67.5kgm/s = 6.0kg v +11.25kgm/s
67.5kgm/s - 11.25kgm/s = 6.0kg v
56.25 kgm/s = 6.0kg v
v = 56.25kgm/s/6.0kg
v = 9.375m/s
v = 9.4m/s
The driver was cut in half.
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