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Phy 211: General Physics I
Ch 9: Brad & Angelina Do Physics
Momentum & Impulse
Momentum:
Brad (80 kg) and Angelina (50 kg) enjoy a relaxing
drive across the south of France in their red
sports car (600 kg).
From rest, they accelerate to a cruising speed of 25
m/s then come to rest at an upcoming stop sign.
Hmm. South
of France.
Descartes. A
coincidence?
I think not…
What could possibly go wrong? …
Questions
1.
What is Brad and Angelina’s combined momentum (including car) at
the stop first sign?
2.
What is their combined momentum at cruising speed?
3.
What are Brad and Angelina’s momentum, respectively, at cruising
speed?
4.
Calculate Brad, Angelina and the car’s individual and combined
impulse as they go from rest to cruising speed.
5.
If it takes them 8 seconds to get to cruising speed, what is the
average net force exerted on Brad, Angelina and the car?
6.
What is the road’s net impulse as Brad, Angelina and the car go from
rest to cruising speed? Which of Newton’s Laws explains this
phenomenon?
7.
What is the impulse Angelina exerts on her car seat as the car
accelerates?
Unexpected Coincidence:
In a hurry for a coffee “date”
with a French mime, Brad’s
jilted ex-wife, Jennifer Aniston
(45 kg), speeds along at 30
m/s in her blue convertible
(800 kg). Unfortunately, she
doesn’t see the red sports car
in the intersection ahead of
her.
v1 =30 m/s
v2=10 m/s
Scenario 1: Inelastic Collision
Fast approaching the intersection, Jennifer’s convertible collides head-on into
the side of Brad and Angelina’s car. During the impact, Jennifer’s car attaches
to Brad and Angelina’s car and both vehicles are thrust through the intersection.
1.
What is the linear momentum of Jennifer (and her car) just
before impact?
2.
What is the momentum of Brad, Angelina (and their car) just
before impact?
3.
What is the combined momentum of this system
immediately after impact?
4.
What is the velocity vector for each vehicle immediately
following impact?
5.
Calculate the impulse vector for each vehicle (including
drivers) due to the collision?
6.
Suppose the impact lasts for 0.5 sec. What is average
impact force exerted on each vehicle?
Concept Questions
1.
How does the impact force received by Jennifer’s vehicle
compare with the force received by Brad and Angelina’s?
2.
How does the acceleration (due to impact) of Jennifer’s
vehicle compare with the acceleration of Brad and
Angelina’s? Calculate the respective accelerations.
3.
If Jennifer were driving a 2500 kg SUV instead of a small car,
would her vehicle receive more, less, or the same impact
force as Brad and Angelina’s car? Explain.
Scenario 2: Elastic Collision
Alternatively, as Jennifer’s car collides with Brad and Angelina’s, the impact
knocks Brad and Angelina’s car off their path but vehicles do not become
attached and remain independent of each other.
1.
What is the combined momentum of this system immediately following impact?
2.
What is the total momentum for the 2 vehicle system, just after impact?
3.
Calculate the velocity for the system pre-impact.
4.
What is the KE of each vehicle (w/passengers), respectively, prior to impact?
5.
Calculate the total KE for the 2 vehicle system, just after impact.
6.
Express the post-impact total momentum and KE by components.
7.
Calculate the system velocity post-impact.
8.
What is the velocity of each vehicle (w/passengers), respectively, immediately
following impact? (refer to textbook)
9.
What is the linear momentum of each vehicle (w/passengers), respectively,
immediately after impact?
10.
What is the KE of each vehicle (w/passengers), respectively, immediately after
impact?
Concept Questions
1.
How does the combined KE (before) of the vehicles compare to after the
Elastic Collision scenario?
2.
Explain the reason for the discrepancy between the before-after KE’s for
the inelastic vs. elastic collision.
3.
How does the impact force received by Jennifer’s vehicle compare with
the force received by Brad and Angelina’s?
4.
How does the acceleration (due to impact) of Jennifer’s vehicle compare
with the acceleration of Brad and Angelina’s? Calculate the respective
accelerations.
5.
If Jennifer were driving a 1500 kg SUV instead of a small car, would her
vehicle receive more, less, or the same impact force as Brad and
Angelina’s car? Explain.
Conclusions
• Linear momentum is conserved before, during and
following both elastic and inelastic collisions (neglecting
external forces such as drag)
• Linear momentum is exchanged between the colliding
bodies:
– Impulse vector associated with one is equal but opposite the
impulse vector associated with the other
• Newton’s 3rd Law is alive and well:
– Impact force is equal (but oppositely directed) between both
bodies involved in a collision regardless of mass or collision type
• KE is not conserved during inelastic collisions
• KE is conserved during elastic collisions