1. Ch 9: Brad & Angelina Do Physics Momentum & Impulse
Phy 211: General Physics I
Ch 9: Brad & Angelina Do Physics
Momentum & Impulse

2. Hmm. South of France. Descartes. A coincidence? I think not…
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? …

3. Questions
What is Brad and Angelina’s combined momentum (including car) at the stop first sign?
What is their combined momentum at cruising speed?
What are Brad and Angelina’s momentum, respectively, at cruising speed?
Calculate Brad, Angelina and the car’s individual and combined impulse as they go from rest to cruising speed.
If it takes them 8 seconds to get to cruising speed, what is the average net force exerted on Brad, Angelina and the car?
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?
What is the impulse Angelina exerts on her car seat as the car accelerates?

4. Unexpected Coincidence:
v1 =30 m/s
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.
v2=10 m/s

5. 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.
What is the linear momentum of Jennifer (and her car) just before impact?
What is the momentum of Brad, Angelina (and their car) just before impact?
What is the combined momentum of this system immediately after impact?
What is the velocity vector for each vehicle immediately following impact?
Calculate the impulse vector for each vehicle (including drivers) due to the collision?
Suppose the impact lasts for 0.5 sec. What is average impact force exerted on each vehicle?

6. Concept Questions
How does the impact force received by Jennifer’s vehicle compare with the force received by Brad and Angelina’s?
How does the acceleration (due to impact) of Jennifer’s vehicle compare with the acceleration of Brad and Angelina’s? Calculate the respective accelerations.
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.

7. 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.
What is the combined momentum of this system immediately following impact?
What is the total momentum for the 2 vehicle system, just after impact?
Calculate the velocity for the system pre-impact.
What is the KE of each vehicle (w/passengers), respectively, prior to impact?
Calculate the total KE for the 2 vehicle system, just after impact.
Express the post-impact total momentum and KE by components.
Calculate the system velocity post-impact.
What is the velocity of each vehicle (w/passengers), respectively, immediately following impact? (refer to textbook)
What is the linear momentum of each vehicle (w/passengers), respectively, immediately after impact?
What is the KE of each vehicle (w/passengers), respectively, immediately after impact?

8. Concept Questions
How does the combined KE (before) of the vehicles compare to after the Elastic Collision scenario?
Explain the reason for the discrepancy between the before-after KE’s for the inelastic vs. elastic collision.
How does the impact force received by Jennifer’s vehicle compare with the force received by Brad and Angelina’s?
How does the acceleration (due to impact) of Jennifer’s vehicle compare with the acceleration of Brad and Angelina’s? Calculate the respective accelerations.
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.

9. 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