Download change in momentum

Momentum
Notes (HRW p196)
Momentum
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Definition
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The measure of how difficult it is to stop a moving
object
Mass in Action!
Formula
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p = mass * velocity, or
p = mv
Units
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kg.m/s
Momentum is a vector!
Mass in Action!
Example
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Q: What is the momentum of a 1000 kg Civic
traveling at 30 m/s?
• p = mass x velocity = m x v
• p = 1000 x 30 = 30,000 kg.m/s
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Q: What is the momentum of a 100,000 kg
locomotive traveling at 30 m/s?
• P = mass x velocity
• P = 100,000 x 30 = 3,000,000 kg.m/s
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Q: What is the momentum of a 40,000 ton
(40,000,000 kg) oil tanker traveling at 5 m/s?
• P = m * v = 40,000,000 * 5
• P = 200,000,000 kg.m/s
Mass in Action!
Impulse
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Definition
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The product of the force (F) acting on an object and
the duration of the force (t)
Formula
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Impulse = F * t
Units
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Newtons.seconds (N.s)
Examples
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Striking a golf/foot/base ball
Seatbelts (how do they work?)
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Auto safety developments since 50’s
Mass in Action!
Impulse Example
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Example: Wall exerts a force of 10,000 N on
the van. The contact time is 0.01 s. What is the
impulse?
Solve: Impulse = F * t = 10,000 * 0.01
• Impulse = 100 N-s
Mass in Action!
Ex. Impulse = Momentum Change
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Impulse = change in momentum (final – initial)
Impulse = 0 – mv
Ft = -mv (momentum is a vector!)
F = mv/t (force felt is the momentum/duration of the
applied force)
Mass in Action!
Impulse and Momentum Change
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According to Newton’s 2nd Law
• The application of a net force on an object will
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result in the object accelerating (aka changing
velocity)
F = ma = m(Δv/t) = m(vf – vo)/t, but
Ft= mvf – mvo = pf – po thus
Ft (or impulse) = change in momentum
Ft = Δmv = mΔv
F = mΔv/t
F = m(vf – v0)/t
(Newton’s 2nd law in
momentum terms)
Mass in Action!
Example – Madness!
Mass in Action!
Impulse Example
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A 1000 kg Civic is traveling at 30 m/s and
accelerates to 40 m/s in 10 seconds.
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What is the momentum of the car before accelerating?
• po = m*v = 1000 * 30 = 30,000 kg.m/s
What is the momentum of the car after accelerating for
10 seconds?
• pf = m*v = 1000*40 = 40,000 kg.m/s
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What is the change in momentum?
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What is the impulse?
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What is the net force that causes the change?
• Δp = pf – po = 40,000 – 30,000 = 10,000 kg.m/s
• J = Change in momentum = 10,000 kg.m/s
• F = change in momentum/time = 10,000/10 = 1,000 N
Mass in Action!
F*t = change in momentum = mΔv
Impulse Example
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A 1000 kg Civic is traveling at 30 m/s
and hits a lamp post.
• What is the momentum of the car while
moving?
• po = m*v = 1000*30 = 30,000 kg.m/s
• What is the momentum of the car after hitting
the post?
• pf = m*v = 1000*0 = 0 kg.m/s
• What is the change in
momentum?
• Δp = pf – po = 0 – 30,000 = -30,000 kg.m/s
Mass in Action!
Impulses and Contact Time
How does momentum of the vehicle relate to the impulse in the 2
scenarios below?
Force is spread over a longer duration
Force is spread over a shorter duration!
Mass in Action!
Summary: Momentum - Impulse
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Interrelated
• Momentum
• Impulse
• Change in momentum
IMPULSE
Force * time
F*t
Mass in Action!
Change in
momentum
F*t = m(vf – vo)
Momentum
Δp = mvf - mvo
Summary
Mass in Action!
Practice
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A stationary 0.12 kg hockey puck is hit
with a force that lasts for 0.01 seconds
and makes the puck move at 20 m/s.
With what force was the puck hit?
Impulse = Change in momentum
• Ft = mΔv = m(vf – vo)
• F = mΔv/t
• F = 0.12 (20 – 0)/0.01 = 240 N
Mass in Action!
Practice
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If a 5kg object experiences a 10 N force
for 0.1 second, what is the change in
momentum of the object?
Solve
• Change in momentum = impulse
• Impulse = F*t
• Change in momentum = F*t = 10*0.1 = 1N-s
Mass in Action!
Practice
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A 50 kg driver of a sports car is traveling at
35 m/s when she hits a large deer. She
strikes the air bag/seatbelt combination that
brings her body to a stop in 0.5 seconds.
• What average force does the bag/belt exert on
her?
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Solve: m=50, vo=35, vf=0, t=0.5, F=?
• F = m*(vf-vo)/t
• F = 50*(-35)/0.5 = -3500 N
Mass in Action!
Practice (continued)
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What if the driver in the previous
example was not wearing a seatbelt and
there were no airbags, and the
windshield stopped her head in 0.002 s.
• What is the average force on her head?
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Solve
• F = 50*-35/0.002 = -875,000 N!!!
Mass in Action!
Conservation of Momentum
Sum of the momenta of all elements before the event = Sum of
the momenta of all elements after the event
Momentum Before firing = p(rifle) + p(bullet) = 0
Momentum After firing = p(rifle) + p(bullet) = 0
After firing, the opposite momenta cancel – direction is
important in vector arithmetic!
Mass in Action!
Conservation of Momentum –
Collisions (aka events)
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2 basic types of collisions for analysis
• Elastic
• Bodies collide and bounce apart – no energy loss
• Bowling ball/pin
• Pool
• Inelastic
• Bodies collide and stick together – some energy
transformation into heat
• Auto rear-ender
• Picking up an object (combining)
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Real world – a bit of both!
Mass in Action!
Momentum Table
Before vs After
BEFORE
Object 1
Object 2
Total Momentum
Mass (m)
m1
m2
Velocity (v)
v1
v2
Momentum
m1v1
m2v2
m1v1 + m2v2
AFTER
Object 1
Object 2
Total Momentum
Mass (m)
m1
m2
Velocity (v)
v1
v2
Momentum
m1v1
m2v2
m1v1 + m2v2
Equate the total momentum (before) with the total momentum (after) to
solve!
Mass in Action!
Practice using table
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A 1000 kg Honda @ 30 m/s collides (head-on
glancing blow) with a 2000 kg Camry @ 20
m/s. If the Honda continues @ 20 m/s,
• what is the speed of the Camry after the impact?
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Solve: Honda, Camry, collision
• Total momentum (before) = Total momentum (after)
• phonda + pcamry = phonda + pcamry
• 1000*30 + 2000*(-20) = 1000*20 + 2000*v
• 30,000 – 40,000 = 20,000 + 2000v
• v = -15 m/s (negative direction)
Mass in Action!
Practice using table
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A 200 kg astronaut leaves the Shuttle for a
space walk and while stationary his tether
breaks. To return to the craft he throws a 2
kg hammer @ 3m/s directly away from the
shuttle.
• What is his returning speed?
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Solve: astronaut, hammer, throw
• pastro + phammer (before) = pastro + phammer (after)
• 200*0 + 2*0 = 200*v + 2*3
• v = -200/6 = -0.03 m/s
Mass in Action!
Practice using table
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A 500 kg bumper car @ 5 m/s runs into the
back of a similar car @ 2 m/s. If the 2nd car
bounces forward at 4 m/s,
• What is the speed of the 1st car?
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Solve: bumper car #1, #2, collision
• (p1 + p2)before = (p1 + p2)after
• 500*5 + 500*2 = 500*v + 500*4
• 2500 + 1000 = 500v + 2000
• v = 3 m/s
Mass in Action!