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Transcript of Take out tables. On a separate sheet: Make a list of every equation we’ve already used in this...
Take out tables.
On a separate sheet:
Make a list of every equation we’ve already used in this class that has the velocity term in it.
Here is your choice:
a. I toss a bullet at you.
b. I shoot a bullet at you from a gun.
Which is more dangerous to you?
Why?
Linear Momentum&
Impulse
Linear Momentum = mass in motion
A measure of how hard it is to stop an object.
It is like a quantity of motion.
How is it different from inertia?
Momentum (p) depends on: mass & velocity of object.
p = mv m in kg
v in m/s
Units are … kg m no name.
s
Momentum is aVector Quantity
Same direction as velocity
All Energy KE too is a scalar
Ex 1. A 2250 kg pickup truck has v = 25 m/s east. What is the truck’s momentum?
p = mv = (2250 kg)(25 m/s)
= 5.6 x 104 kg m
s
Change in momentum - accl occurs any time an object changes
velocity (speed or direction).
Momentum Change &Newton’s 2nd Law
• F = ma
• F = m(v/t)
• Ft =mv m (vf - vi) for const mass.
• Ft = p Impulse.p = Change in momentum
Equations of Momentum Change
• J =Ft = p Impulse = change momentum.
• pf – pi.
p = mvf – mvi
• for velocity change with constant mass can factor out mass you can write,
• m (vf - vi) or mv.
Force is required to change velocity or momentum of a body in motion.Force must be in contact for some time.
Increased force & contact time on object give greatest impulse p = mv.
Hit a homerun needs large impulse. The more contact time, the less force needed to give same impulse p.
Impulse (J) is the momentum change. It has the same units.
kg m or Ns s
It is like force but includes a contact time component!
Ex 2. How long does it take an upward 100N force acting on a 50 kg rocket to increase its speed from 100 to 150 m/s?
F = 100 Nv = 50 m/sm = 50 kg
Ft = mv
t = mv F
50 kg(50 m/s) 100 kg m/s2 = 25 s.
Concept: A pitcher throws a fastball to a catcher. Who exerts a larger force on the ball? Explain.
Concept: Explain, in terms of impulse and momentum, how airbags help avoid injury in a car crash.
Examples of Impulse/Change in Momentum
• Baseball batter swinging through ball.
• Applying brakes of car over time to stop.
Ex 3. How long does it take a 250 N force to increase to speed of a 100 kg rocket from 10 m/s to 200 m/s?
Ft = mv t = mv F
F = 250 Nm= 100 kgv =190 m/s
t = 100kg(190m/s) 250 kg m/s2. = 76 s.
Ex 4. The speed of a 1200 kg car increases from 5 to 29 m/s in 12 s. What force accelerated the car?
Ex 5: A 0.4 kg ball is thrown against a wall with a velocity of 15 m/s. If it rebounds with a velocity of 12 m/s:
a) what was its v?b) What was its p?
v = vf – vi.
-12 m/s – (15 m/s) = - 27 m/s.
p = mv
= 0.4kg(27m/s)
=10.8 kg m/s
• Running with momentum. 15 min.
• https://www.youtube.com/watch?v=jLIyDfkQcsk
• Relaxing with impulse.13 minutes.
• https://www.youtube.com/watch?v=0nOHLThv2mw
Understanding Car Crashes 22 minstart 8:53
• Hewitt Momentum 4:20
• https://www.youtube.com/watch?v=2FwhjUuzUDg
http://www.youtube.com/watch?v=yUpiV2I_IRI
Hwk read text 208 – 211
do pg 214 #1- 4 conceptsdo p 211 #1 - 4. Impulse prbs.
Also worksheet “Impulse Momentum”
Which are units of Impulse?
NmN/sNsN/m
A ball mass 0.10 kg is dropped from 12-m. Its momentum just as it strikes the ground is:
1.5 kgm/s1.8 kgm/s2.4 kgm/s4.8 kgm/s
A 0.060-kg tennis ball, initially moving at 12 m/s, is struck by a racquet causing it to move in the opposite direction at a speed of 18 m/s. What is the impulse exerted by the racquet on the ball?
0.36 kgm/s0.72 kgm/s1.1 kgm/s1.8 kgm/s
Graphs
Constant force f - t graph:p /Impulse is area under curve Ft.
For
ce N
Non-Constant ForceForce vs. time graph. The area under the curve =
impulse or p change in momentum.
What is the impulse during the 9 seconds of contact?
225 Ns
Consv Momentum Demos.
Conservation of Momentum
If no external force acts on a closed system, the total momentum remains unchanged even if objects interact.
What is a system?
Two or more objects that interact in motion. One may transfer part or all of its momentum to the other(s).
Common examples: collisions, explosions.
One Ball transfers all its momentum.
The astronaut transfers part of his momentum to the second astronaut.
Conservation of Momentum Calc’s
• Total momentum before = total after interactions.
• Collisions.
• Explosions
• Pushing apart.
Pbefore = pafter
m1v1 + m2v2 = m1fv1f + m2fv2f
v1 and v2 velocities for objects one and two.
m1 and m2 masses of objects
To Calculate:
Recoil From Explosions
Recoil illustrates conservation of momentum where initial and
final momentum = 0.0 = p1 + p2.
1. The cannon is 100kg and the cannonball is 5 kg. If the ball leaves the cannon with a speed of 100 m/s, find the recoil velocity of the cannon.
Before Firing After Firingm1v1 + m2v2 = m1fv1f + m2fv2f
0 = (100kg)vcf + (5kg)(100m/s) -500 kgm/s = (100 kg) vcf
- 5 m/s = vcf recoil velocity of cannon
Extra Example – not on sheet
• A 63-kg astronaut is in spacewalk when the tether breaks. The astronaut throws a 10-kg oxygen tank directly away from the spaceship at 12 m/s. Assuming the astronaut was initially at rest, what is his final speed after throwing the tank?
• 1.9 m/s
• Hwk. Read text p 215-218. Do pg 221 #2, and pg 233 #17, 19, 20, 24, 25.
Recoil Hewitt 6:25
https://www.youtube.com/watch?v=1-s8NZ8xKW0
Let’s say a 4 kg fish swimming at 5 m/s, eats a 1 kg fish. What is their final
velocity?
Stick em together problems
Bg fish sm.fish Bg fish sm.fishm1v1 + m2v2 = m1fv1f + m2fv2f
(4kg)(5m/s)+(1 kg)0 =(4kg)v1+(1kg)v2
But the final velocities are equal so factor out the vf:
20 kg m/s = vf (4+1kg)
vf = (20 kg m/s) / (5kg) = 4m/s
Fish lunch Hewitt 4:00
https://www.youtube.com/watch?v=MK0B5hEU7OI
Find the final velocity of the cart and brick together
2. A 2 kg brick is dropped on a 3 kg cart moving at 5.0 m/s.
cart brick cart brickm1v1 + m2v2 = m1fv1f + m2fv2f
(3kg)(5.0m/s) + 0 = (3kg)v1 + (2kg)v2
150 kg m/s = v (3kg + 2 kg)
(150 kg m/s )/5 kg = 3.0 m/s
Elastic & Inelastic Collisions
Totally Elastic: no KE lost at all(to heat, light, sound etc.) Usu. Involves objects that don’t make contact or bounce off.
Totally Inelastic: involves greatest loss of KE. Usu damage done. Most extreme case – objects stick together.
Which is totally elastic? Inelastic?
Inelastic Collisionmc = 1000 kg mt = 3000 kgvc = 20 m/s vt = 0pc = pt =
m1v1 + m2v2 = m1fv1f + m2fv2f (1000kg)(20m/s) + 0 = (1000)v + (3000)v
(20000 kg m/s) = (1000kg + 3000kg)v
(20000 kg m/s) = (4000 kg)v
(20000 kg m/s) = v4000 kg
v = 5 m/s
Elastic Collision mc = 1000 kg mt = 3000 kg
vc = 20 m/s vt = 0
Find final velocity of the car if truck has final velocity of 10 m/s.
m1v1 + m2v2 = m1fv1f + m2fv2f
(1000kg)(20m/s) + 0 =(1000kg)vc+(3000kg)(10m/s)
20,000 kg m/s = (1000kg)vc+30000 kg m/s
20,000 kg m/s – 30,000 kg m/s = vc
(1000kg)
- 10 m/s = vc
Do Now: On July 4th my family likes to shoot off fireworks. One rocket was shot straight up, climbed to a height 18-m and exploded into hundreds of pieces in all directions at its highest point.
Thinking about conservation laws, think about the rocket at its highest point just before & just after it explodes:
How does the rocket’s momentum compare before & after the explosion?
How does its KE compare compare before & after the explosion?
Inelastic CollisionsStick em together
KE “lost” converted
Elastic Collisions – no KE lost.Bounce off each other.
• Pg 233 #17, 19, 20, recoil prbs24, 25.
• Sentences, equations, show work w/units.
In classpg 221 #1 write out and hand in to
be graded.
and do pg 219 #1 – 4 calcs
Film Car Crashes or Running with momentum.
http://www.youtube.com/watch?v=yUpiV2I_IRI