Download Lecture 16 (Feb 29) - West Virginia University

Chapter 6: Momentum and Impulse
WEST VIRGINIA UNIVERSITY
Physics
Impulse
Changing an object’s momentum requires the continuous application of a force during
a time interval Δt:
Definition of Impulse:
unit: kg · m/s
F
m
vi
m
vf
Impulse is the change of an object’s momentum
WEST VIRGINIA UNIVERSITY
Physics
Example problem: Car crash
In a crash test, a car of mass 1500 kg collides with
a wall and rebounds as shown in the figure. The
initial and final velocities of the car are vi = -15 m/s
and vf = 2.6 m/s, respectively. If the collision lasts
for 0.15 s, find
A. the impulse delivered to the car due to the
collision.
B. the size and direction of the average force
exerted on the car.
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Physics
The Physics of Injuries
Let’s do an experiment (2 parts):
1. Take your fist and hit the table in front of you.
Don’t hit too hard!
→ That hurts!
2. Now look at your neighbor….
Hit him/her against the arm. Move your fist at
roughly the same speed as before.
→ That does not hurt so much!
Why not?
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Physics
The Physics of Injuries
The change in momentum, i.e. the impulse, is the same in both experiments, since the
initial velocity of your fist (before the collision) was the same and the final velocity
was the same (vf = 0 m/s) in both experiment.
The difference was the surface material your fist crashed into: Hard table top vs. soft arm!
In case of the soft material (arm) your fist had more time to slow down.
If the impulse is the same in both experiments, the force acting on your fist will be
smaller, if the material is soft, since Δt is larger.
This is the reason, why boxers wear boxing gloves and airbags are used in cars - to
prevent serious injuries!
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Physics
Why seat belts can save lives
A 75 kg passenger drives a car at 27 m/s (60
mi/h) and does not wear a seat belt.
His car crashes into a tree, he flies through
the car and is stopped by a hard unpadded
dashboard in 0.01s.
This force will kill the guy!
If he wears a seat belt, Δt is increased to typically about 0.15s. The impulse remains the
same, but the force will decrease to 9800 N. This can be survived!
WEST VIRGINIA UNIVERSITY
Physics
Summary
• Definition of linear momentum:
Unit: kg · m/s
Momentum is a vector quantity. It points into the same direction as the object’s velocity.
• Relation between momentum and kinetic energy:
• Relation between force and impulse:
• Definition of impulse:
Impulse corresponds to a change of momentum during a time interval Δt.
F
m
vi
m
vf
WEST VIRGINIA UNIVERSITY
Physics
Conservation of momentum in 1d
Two objects (masses: m1, m2) moving at initial velocities v1i
and v2i collide.
During the time of collision, Δt, object 1 exerts a force F12
on object 2 and object 2 exerts a force F21 on object 1. There
are no other external forces!
Impulse momentum theorem for m1 and m2:
Newton’s third law says:
WEST VIRGINIA UNIVERSITY
Physics
Conservation of momentum in 1d
This equations says that the total momentum of the
system will be conserved, if there is no effective
external force acting on it.
Here, the system consists of the two colliding
objects.
The reason for the conservation of momentum is
Newton’s 3rd law, i.e. F12 = -F21.
Important: The total momentum is conserved, but not the individual momenta!
The momentum (velocities) of the colliding objects typically change as a consequence of
the collisions.
WEST VIRGINIA UNIVERSITY
Physics
Example problem: Conservation of momentum
The head of a 200 g golf club is traveling at 55
m/s just before it strikes a 46 g golf ball at rest
on a tee. After the collision, the club head
travels (in the same direction) at 40 m/s.
Find the speed of the golf ball just after impact.
WEST VIRGINIA UNIVERSITY
Physics
Example problem: Astronaut in space
An astronaut in his/her space suit has a total mass of 87 kg, including suit and oxygen
tank. His/her tether line loses its attachment to her spacecraft, while he/she is on a
spacewalk. Initially at rest with respect to her spacecraft, she throws her 12 kg oxygen
tank away from her spacecraft with a speed of 8 m/s to propel herself back toward it.
Determine the maximum distance she can be from the craft and still return within 2 min
(the amount of time the air inside her helmet remains breathable).
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Physics
Conservation of momentum in 2d
If the objects can move in 2 dimensions and external forces can be neglected, the equation
for momentum conservation will become a vector equation:
The momentum is then conserved for every component separately. In this case:
x-component:
y-component:
WEST VIRGINIA UNIVERSITY
Physics
Example problem: Collision at an Intersection
A car with mass 1500 kg traveling east at a
speed of 25 m/s collides at an intersection with a
2500 kg van traveling north at a speed of
20 m/s. After the collisions both cars stick
together and the resulting wreckage propagates
at a common speed.
Find the magnitude and the direction of of the
velocity of the wreckage.
Neglect Friction, i.e. any external forces.
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Physics
Summary
• If no effective external force acts on a system of objects,
its total momentum will be conserved.
•
• In 2d, this equation becomes a vector equation
and momentum conservation is valid for each
component separately.
• Conservation of momentum can be explained by
by Newton’s third law, i.e. all internal forces
compensate each other.
• Momentum conservation can be used to describe
collision processes, i.e. calculate initial and final
velocities of the collision partners.
WEST VIRGINIA UNIVERSITY
Physics