Download VI. Conservation of Energy and Momentum C. Momentum 12. The

VI.
Conservation of Energy and Momentum
C.
Momentum
12.
13.
14.
15.
The Nature of Momentum
The Conservation of Momentum
Inelastic Collisions
Elastic Collisions
Why is a bullet that is thrown not as dangerous as a bullet that is fired from a rifle?
_______________________________________________________________________________
Momentum is ________________ in motion. _________________________ is the product of the
mass of a moving body and its velocity.
momentum () = m  v
SI Unit for momentum: ______________
Example 1:
Determine the momentum of an F 150 truck moving northward at 45 mph. Assume a weight
5000 pounds
1 mile = 1.6 km
1 kg = 2.2 pounds
Example 2:
How fast (in mph) would a Mini Cooper (2500 pounds) need to be traveling to have the same
momentum as the truck in Example 1?
Example 3:
Calculate the momentum of the Titanic, of mass 4.2 x 107 kg, moving at 14 knots
(1 knot = 1.852 km/h).
Momentum of an object can be changed by __________________. This requires a ___________. The
result is not instantaneous, but requires _____________.
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_________________________ is the product of a force and the time interval during which it acts.
Unlike most of our calculations, impulse is NOT defined by just one variable. Impulse is nothing more than
a ____________________ in momentum.
impulse (Ft) = m  v.
SI Unit for momentum: ______________
Impulse-Momentum Theorem :
Ft = p
In simple terms, a ___________ force acting for a long time can produce the same change in momentum as
a large force acting for a ________ time
Example 4:
A hockey puck has a mass of 0.115 kg and is at rest. A hockey player makes a shot, exerting
a constant force of 30.0 N on the puck for 0.16 s. With what speed does it head toward the
goal?
Example 5:
If the momentum of the NASA space shuttle as it leaves the atmosphere is
3.75 x 108 kg m/s, and its mass is 75,000 kg, what is its speed?
Example 6:
A 2200-kg sport utility vehicle traveling at 26 m/s can be stopped in 21 s by gently applying
the brakes, in 5.5 s in a panic stop, or in 0.22 s if it hits a concrete wall. What average force
is exerted on the SUV in each of these stops?
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Law of Conservation of Momentum
A 5.0 kg bowling ball with a velocity of 6.0 m/s strikes a 1.5 kg standing pin squarely. If the ball
continues on at a velocity of 3.0 m/s what will be the velocity of the pin after the collision?
A 5 kg bowling ball is rolling in the gutter towards the pins at 2.4 m/s. A second bowling ball with a
mass of 6 kg is thrown in the gutter and rolls at 4.6 m/s. It eventually hits the smaller ball and the 6 kg
ball slows to 4.1 m/s. What is the resulting velocity of the 5 kg ball?
Two people are practicing curling. The red stone is sliding on the ice towards the west at 5.0 m/s and has
a mass of 17.0 kg. The blue stone has a mass of 20.0 kg and is stationary.
After the collision,
stone A moves east at 1.25 m/s. Calculate the momentum and velocity of the blue stone after the
collision.
A 50-g golf ball is struck with a club. The force on the ball varies from zero (when contact
is made) up to a maximum value (when the ball is deformed) and then back to zero (when
the ball leaves the club). Assume that the ball leaves the club’s face with a velocity of +44
m/s.
A.
Estimate the impulse due to collision.
B.
Estimate the duration of the collision.
C.
Estimate the average force on the ball.
An inelastic collision between two particles is one in which part of their kinetic energy is transformed to
another form of energy. The total amount of energy remains the same. We will consider that the objects
that collide do not bounce off each other.
An elastic collision between particles is one in which the total kinetic energy of the particles is conserved.
We will consider that the objects that collide do bounce off each other.
inelastic:
m1 v 1
+
m2 v 2
=
m1+2  v1+2
elastic:
m1 v 1
+
m2 v 2
=
m1Av1A
+
m2Av2A
We will assume energy is conserved. Momentum is directly related to energy. Therefore, momentum is
conserved. How does the momentum equation differ from the kinetic energy equation?
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Example:
A 59-kg physics student jumps off the back of her Laser sailboat, of mass 42 kg. After she
jumps, the Laser is found to be traveling at 1.5 m/s. What is the speed of the student?
Example:
The same physics student jumps off the back of her Laser again, but this time the Laser is
already traveling at 3.1 m/s before she jumps. If the physics student jumps off with a
speed of 2.1 m/s, how fast is the Laser going after she jumps?
Example:
The Titanic hit an iceberg estimated to be half of her mass. Before hitting the iceberg, the
Titanic was estimated to be going 22 knots (11.3 m/s). After hitting the iceberg, the
Titanic was estimated to be going about 6.0 knots (3.1 m/s). How fast was the iceberg going
after the collision?
Example:
A 59 kg physics student is riding her 220 kg Harley at 12 m/s when she has a head-on
collision with a 2.1 kg pigeon flying the opposite direction at 44 m/s. The bird is still on the
motorcycle after the collision. How fast is the motorcycle going after the collision?
Example:
A BC Ferry, or mass 13,000,000.0 kg, is traveling at 11 m/s when the engines are put in
reverse. The engines produce a force of 1.0 x 106 N for a period of 20.0 seconds. What is
the magnitude of the impulse from the engine? What is the new momentum of the ferry?
What is the new velocity of the ferry?
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References:
Trinklein, F. E. Modern Physics (TE). Austin: Holt, Rinehart and Winston, 1992.
Chapter 9 of Zitzewitz, P. W. Glencoe Physics: Principles and Problems. New York:
Glencoe/McGraw-Hill, 2002.
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