Transcript Momentum Lecture - Petoskey Public Schools

Momentum and
Impulse
What is Momentum?
Momentum – The product of the mass and
velocity of an object. Has magnitude and
direction.
Momentum = p = mv
P = momentum
M = mass
V = velocity
Units: kg∙m/s
Inertia?
• Remember Newton’s 1st Law?
• An object at rest will stay at rest
and
• An object in motion will stay in motion in
the same speed and direction unless
acted on by an outside force.
What’s Inertia Got to Do with It?
• Momentum is directly related to the
second part of Newton’s 1st Law
– An object in motion stays in motion (same
speed and direction) unless acted on by a
force
Let’s practice
• A 1200 kg car drives west at 25 m/s for 3
hours. What is the car’s momentum?
• Identify the variables:
– 1200 kg = mass
– 25m/s, west = velocity
– 3 hours = time
P = mv = 1200 x 25 = 30000 kg m/s, west
How hard is it to stop a moving
object?
Impulse: Product of force and time interval
during which the force acts. Impulse
equals momentum change.
Impulse = FΔt
F = force (N)
Δt = time elapsed (s)
Units: N∙s
How hard is it to stop a moving
object?
• Using Newton’s 2nd Law we get
Impulse = change in momentum
FΔt= mΔv
Why does an egg break or not
break?
• An egg dropped on a tile floor breaks, but an
egg dropped on a pillow does not. Why?
FΔt= mΔv
In both cases, m and Δv are the same.
If Δt goes up, what happens to F, the force?
Right! Force goes down. When dropped on a
pillow, the egg starts to slow down as soon as it
touches it. A pillow increases the time the egg
takes to stops.
Practice Problem
A 57 gram tennis ball falls on a tile floor. The ball
changes velocity from -1.2 m/s to +1.2 m/s in
0.02 s. What is the average force on the ball?
Identify the variables:
Mass = 57 g = 0.057 kg
Δvelocity = +1.2 – (-1.2) = 2.4 m/s
Time = 0.02 s
using FΔt= mΔv
F x (0.02 s) = (0.057 kg)(2.4 m/s)
F= 6.8 N
Car Crash
Would you rather be in a
head on collision with an
identical car, traveling at
the same speed as you, or
a brick wall?
Assume in both situations you
come to a complete stop.
Take a guess
http://techdigestuk.typepad.com/photos/uncategorized/car_crash.JPG
Car Crash (cont.)
The answer is…
It Does Not Matter!
Look at FΔt= mΔv
In both situations, Δt, m, and Δv
are the same! The time it
takes you to stop depends on
your car, m is the mass of
your car, and Δv depends on
how fast you were initially
traveling.
Conservation of Momentum
Conservation of Momentum
• Just like energy, momentum is conserved.
• The total momentum at the start will equal
the total momentum at the end
Vectors!
• Remember that momentum is a vector
value, so if two momentums are in
opposite directions, they are opposite
signs and end up cancelling (at least in
part)
Two Flavors!!
• Collisions may be
– Elastic – the objects completely bounce off
each other
Billiards (pool) ball have elastic collisions
– Inelastic – the objects stick together at the
collision and travel together thereafter
Car Crashes have become inelastic with
better engineering
Momentum Formulas
• The standard formula for momentum is
• P=mv
• What happens if we have two objects that collide
and bounce off each other…..elastic??
• We can make a formula for this due to the
conservation of momentum!
• M1V1i + M2V2i = M1V1f + M2V2f
Practice Elastic
• A 50 kg skater traveling at 10 m/s hits a 40 kg
skater sitting still, imparting all his momentum
into the 2nd skater. What is the velocity of the
2nd skater?
• M1V1i + M2V2i = M1V1f + M2V2f
• (50 kg)(10 m/s) + (40 kg)(0 m/s) = (50 kg)(0 m/s) + (40 kg)V2f
• (500 kg*m/s) + (0 kg*m/s) = (0 kg*m/s) + (40 kg)V2f
• 12.5 m/s = V2f
Practice Problem
• A 50 kg skater traveling at 10 m/s hits a 40
kg skater sitting still. The 1st skater ends
up at 2 m/s. What is the velocity of the 2nd
skater?
M1V1i + M2V2i = M1V1f + M2V2f
(50 kg)(10 m/s) + (40 kg)(0 m/s) = (50 kg)(2 m/s) + (40 kg)V2f
(500 kg*m/s) + (0 kg*m/s) = (100 kg*m/s) + (40 kg)V2f
10 m/s = V2f
Practice Problem
• A 50 kg skater traveling at 20 m/s hits a 40 kg
skater moving in the same direction at 3 m/s.
The 1st skater ends up at 5 m/s. What is the
velocity of the 2nd skater?
M1V1i + M2V2i = M1V1f + M2V2f
(50 kg)(20 m/s) + (40 kg)(3 m/s) = (50 kg)(5 m/s) + (40 kg)V2f
(1000 kg*m/s) + (120 kg*m/s) = (125 kg*m/s) + (40 kg)V2f
24.875 m/s = V2f
Inelastic Collision Formula
• Since the objects travel together after the
collision, we have a slightly different formula for
inelastic collisions
M1V1i + M2V2i = (M1+ M2)Vf
• This shows the final momentum is created by
the total mass of the two objects together
Practice Inelastic
• A 50 kg skater traveling at 20 m/s picks up
a 40 kg passenger skating sitting still, what
is the velocity of the two skaters?
M1V1i + M2V2i = (M1+ M2)Vf
(50 kg)(20 m/s) + (40 kg)(0 m/s) = (90 kg)Vf
(1000 kg*m/s) + (0 kg*m/s) = (90 kg)Vf
11.1 m/s = Vf
Practice Problem
• A 50 kg skater traveling at 20 m/s picks up
a 40 kg passenger skating in the same
direction at 5 m/s, what is the velocity of
the two skaters?
M1V1i + M2V2i = (M1+ M2)Vf
(50 kg)(20 m/s) + (40 kg)(5 m/s) = (90 kg)Vf
(1000 kg*m/s) + (200 kg*m/s) = (90 kg)Vf
13.3 m/s = Vf
Practice Problem
• A 50 kg skater traveling at 20 m/s picks up
a 40 kg passenger skating in the opposite
direction at 5 m/s, what is the velocity of
the two skaters?
M1V1i + M2V2i = (M1+ M2)Vf
(50 kg)(20 m/s) + (40 kg)(-5 m/s) = (90 kg)Vf
(1000 kg*m/s) - (200 kg*m/s) = (90 kg)Vf
8.89 m/s = Vf