chapter 7 momentum. chapter warm up 1. what is a non physics definition of momentum? give an...
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5. What does it mean when a quantity is conserved? 6. How are elastic and inelastic collisions the same? 7. How are elastic and inelastic collisions different?TRANSCRIPT
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Chapter 7
Momentum
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Chapter Warm Up
1. What is a non physics definition of momentum? Give an example. 2. What is the physics definition of momentum? Give an example. 3. How can the momentum of an object be changed?
4. What is impulse?
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5. What does it mean when a quantity is conserved?
6. How are elastic and inelastic collisions the same?
7. How are elastic and inelastic collisions
different?
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Section 1: Linear Momentum
Definition:Inertia in motion
Example:
Symbol:p
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Equation:Momentum = mass x velocityp=mv
Units: p= kg m = kgm
s s
Vector quantity
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Examples:1. A 2250 kg pickup truck has a velocity of
25m/s to the east. What is the momentum of the pickup truck?
5.6 x 104 kgm/s east
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2. A car has a mass of 1210 kg. How fast must it be traveling if its momentum is 2.5 x 103 kgm/s? 2.1 m/s in the direction of travel
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3. A child is riding a bike, and is traveling at a velocity of 4.5 m/s to the northwest. If the momentum of the bike and the child is 1.2 x 102 kg m/s to the northwest, what is the combined mass of the bike and the child?
27 kg
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How can an object’s momentum be changed?change mass or velocity
if change velocity – object accelerates– a force is needed
larger force – larger change in momentum
BUT: TIME FORCE IS APPLIED IS ALSO IMPORTANT
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How about the time the force is applied?apply force briefly to an object – change in momentumapply same amount of force for a longer time– larger change in momentum
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Why????p = mv, but velocity has a time component– so the larger the Δt, the larger the Δv, and the larger the momentum change
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So….A large force over a small time can equal the same momentum change as a smaller force over a longer time
FORCE AND TIME ARE BOTH IMPORTANTThis leads to a new quantity: Impulse
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ImpulseDefinition:
Product of force and time interval during which the force actsCauses momentum to change
Equation: Impulse = FΔt
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But, from NII:F = ma
and from Chapter 2a = Δv/Δt
substitutingF = mΔv/Δt
rearranging FΔt = Δ(mv)So impulse = Δ momentumThis is the Impulse – Momentum Theory
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Section 2: Impulse – Momentum Theory
Definition:Any impulse acting on a system changes the system's momentum. (http://faculty.wwu.edu/vawter/PhysicsNet/Topics/Momentum/ImpulseMomTheorem.html)
Equation:FΔt = Δ(mv)usually written as FΔt = mΔv
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Examples: 1. A 1400 kg car moving westward with a
velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. What force is exerted on the car during the collision?
7.0 x 104 N east
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2. A 0.50 kg football is thrown with a velocity of 15 m/s to the right. If a stationary receiver exerts a force of 3.8 x 102 N to the left when catching the ball, how long did it take the receiver to catch the ball and bring it to a halt?
0.020s
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3. A man drops from rest off a diving board that is 3.0 m above the surface of the water and comes to rest 0.55 s after reaching the water. If the force on the diver is 1.1 x 103 N upward, what is the diver’s mass?
79kg
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So… How do we change the momentum of an object?
change any or allforce of impacttime of impactmass of objectvelocity of object
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Impulse – Momentum in the Real World
Hitting a ball
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Barrels on the Interstate at bridges
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Catching a ball
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Your own examples
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The bottom line: Impact time and impact force are
inversely proportional for the same change in momentum
A moving object has a certain amount of momentum, so if you increase the impact time, you will decrease the impact force ( which is what you usually want)
orIf you decrease the impact time, you will
increase the impact force
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DON’T CONFUSE IMPULSE, IMPACT, AND MOMENTUM!!!!Impact is a forceImpulse is what is applied to an object to change it’s momentumTo bring an object to a stop,impulse applied = change in momentum ( as momentum goes to zero.)
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Check your concepts: 1. Which involves less impulse, a dish falling to
a tile floor, or a dish falling the same distance to a carpet?
Neither– the change in momentum is the same, so the impulse required is the same. Mass doesn’t change, and Δv is a free fall issue, depending on the height.
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2. Why is basketball played on a wood or composite floor rather than concrete?
The wooden or composite floor has more “give”, which increases the impact time, therefore decreasing the impact force, which means the player feels less force on the body.
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3. Why do athletes get injured on artificial grass more often than on real grass?
Same as the basketball floor – the grass increases impact time, so decreases impact force.
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Section 3: Conservation of Momentum
What does conserved mean?The amount of a quantity in a system is not changed during an interactionThe amount you end with must be the same as the amount you started with.
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Conservation LawsEnergy
Energy cannot be created nor destroyed, it merely changes formMatter
Matter cannot be created nor destroyed, it merely changes formMomentum
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Conservation of MomentumIn a closed system, the total amount of momentum is conserved(constant)Momentum can be transferred from one object to another within the system
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To change the amount of momentum of a system, an outside force or impulse must be applied to the system
Internal ones are action-reaction pairs and don’t affect the momentum of the system
sitting in a car and pushing on the dashboard is internal
pushing on the bumper is external
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If there is no net force, there is no net impulse, so no net change in momentum of the system
This leads to the Law of Conservation of Momentum
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In the absence of an external force, the
momentum of a system remains
unchanged
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Equation:m1v1i + m2v2i = m1v1f + m2v2f
m1 = mass of object 1v1i = initial velocity of object 1m2 = mass of object 2v2i = initial velocity of object 2v1f = final velocity of object 1v2f = final velocity of object 2
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Examples:1. A 76 kg boater, initially at rest in a stationary
45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?
4.2m/s to the left
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2. An astronaut is at rest on a space walk when the tether line to the shuttle breaks. The astronaut is able to throw a spare 10.0 kg oxygen tank in a direction away from the shuttle with a speed of 12.0 m/s, propelling the astronaut back to the shuttle with a speed of 1.90 m/s. What is the astronaut’s mass?
63.2kg
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Section 4: CollisionsWhat is a collision? A collision occurs when 2 objects try to
occupy the same space at the same time
IN COLLISIONS, MOMENTUM IS CONSERVED
Net momentum before collision = net momentum after collision
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2 Types of collisions:
Elastic collisions
Inelastic collisions
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Elastic collisions2 objects collide and fly apartmomentum is transferred from one object to the otherExampleBilliard ballsone moving towards the other when collide and bounce apartmomentum is transferred from the one with more initial momentum to the one with less initial momentum
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Equation:m1v1i + m2v2i = m1v1f + m2v2f (look familiar?)
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Examples:1. A 16.0 kg canoe moving to the left at 12.5
m/s makes an elastic head-on collision with a 14.0 kg raft moving to the right at 16.0 m/s. After the collision, the raft moves to the left at 14.4 m/s. Find the velocity of the canoe after the collision. Disregard any effects of the water.
14.1 m/s to the right
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2. A 25.0 kg bumper car moving to the right at 5.00 m/s overtakes and collides elastically with a 35.0 kg bumper car moving to the right. After the collision, the 25.0 kg bumper car slows to 1.50 m/s to the right, and the 35.0 kg car moves at 4.50 m/s to the right. What is the velocity of the 35 kg bumper car before the collision?
2.0m/s to the right
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Inelastic collisions2 objects collide and stick together ( 2 objects become 1 object)
ExampleA person catching a ballWhen the person catches the ball, two objects, a ball and a person, become 1 object a ball-person
Equation: m1v1i + m2v2i = (m1 + m2)vf
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Examples:1. An 1850 kg luxury sedan stopped at a traffic
light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?
7.58 m/s north
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2. A dry cleaner throws a 22 kg bag of laundry onto a stationary 9.0 kg cart. The cart and the laundry bag begin moving at 3.0 m/s to the right. What was the velocity of the laundry bag before the collision?
4.2 m/s to the right
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3. A 47.4 kg student runs down the sidewalk and jumps with a horizontal speed of 4.20 m/s onto a stationary skateboard. The student and the skateboard move down the sidewalk with a speed of 3.95 m/s. What was the mass of the skateboard?
3.0 kg