Physics 8 — Friday, September 11, 2015

I http://positron.hep.upenn.edu/physics8

I Hand in HW2. Average reported time was 3.2 hours. I’ll tryto keep them roughly this length. If you’re not sufficientlychallenged, do the XC problems!

I Pick up HW3 handout (due next Friday).

I Next week, you have two more Mazur chapters to read:Chapter 6 (about relative motion, “reference frames,” etc.)and Chapter 7 (“interactions” — a conceptual prelude toforces). They are “due” Monday and Wednesday, respectively,but the due dates are flexible because of the Rosh Hashanaholiday. A couple of days late is fine, though I imagine thisweekend is easier for reading than midweek.

I As I said Weds, I think this year we’ll just forego the quizzesand instead do a larger number of homework-like problemsthat you’ll work on together in class. It’s more fun that way.

Where are we (going)?

To analyze structures, you need a thorough understanding offorces, torques (a.k.a. “moments” of forces), and vectors.

Where are we (going)?

(Richard Wesley: “A course should tell a story.”)

I To analyze structures, you need a thorough understanding offorces, torques (a.k.a. “moments” of forces), and vectors.

I To understand forces well, you need a solid grasp ofI How forces affect motion.I How different forces relate to one another.I How objects interact with one another via forces.

I In ch2–3, we studied the key concepts of motion: position,velocity, acceleration, etc.

I In ch4–5, we studied two key conservation laws (momentum,energy) and some of the restrictions they place on howcolliding objects can interact with one another.

I Finally in ch8 we’ll discuss forces! We’re preparing your mindfor forces in ch6–7 by learning a few more of the restrictionsimposed, as a consequence of momentum & energyconservation, on how objects can interact with one another.

(We did this at the very end of Wednesday’s class.)

What sort of collision is illustrated by this velocity-vs-time graph?

(A) elastic

(B) inelastic

(C) totally inelastic

(D) explosive separation

(E) can’t tell from giveninformation

(By the way, can you infer the ratio of masses?)

What sort of collision is illustrated by this velocity-vs-time graph?

(A) elastic

(B) inelastic

(C) totally inelastic

(D) explosive separation

(E) can’t tell from giveninformation

(By the way, can you infer the ratio of masses?)

Imagine making two springy devices, each made up of a dozen orso metal blocks loosely connected by springs, and then collidingthe two head-on. Do you expect the collision to be elastic,inelastic, or totally inelastic? (Think about what happens to thekinetic energy.)

(A) elastic

(B) inelastic

(C) totally inelastic

http://youtu.be/SJIKCmg2Uzg

Newton’s cradle: what do you expect to happen if I pull back twoof the spheres and release them?

I Discuss! (No clicking required.)

What do you expect to happen if I put a piece of play doughbetween two of the spheres?

I Discuss! (No clicking required.)

Newton’s cradle: what do you expect to happen if I pull back twoof the spheres and release them?

I Discuss! (No clicking required.)

What do you expect to happen if I put a piece of play doughbetween two of the spheres?

I Discuss! (No clicking required.)

If all three collisions in the figure shown here are totally inelastic,which bring(s) the car on the left to a halt?

(A) I

(B) II

(C) II,III

(D) all three

(E) III

Which of these systems are isolated?

(1) While slipping on ice, a car collides totally inelastically withanother car. System: both cars (ignore friction)

(2) Same situation as in (a). System: slipping car

(3) A single car slips on a patch of ice. System: car

(4) A car brakes to a stop on a road. System: car

(5) A ball drops to Earth. System: ball

(6) A billiard ball collides elastically with another billiard ball on apool table. System: both balls (ignore friction)

(A) (1) only

(B) (6) only

(C) (1) + (3) + (6)

(D) (1) + (2) + (3) + (4) + (6)

(E) (1) + (2) + (3) + (4) + (5)+ (6)

A compact car and a large truck collide head on and sticktogether. (Neither driver is applying the brakes.) Which undergoesthe larger momentum change?

(a) car

(b) truck

(c) The momentum change is the same (in magnitude) for bothvehicles.

(d) Can’t tell without knowing the final velocity of combined mass.

A compact car and a large truck collide head on and sticktogether. (Neither driver is applying the brakes.) Which undergoesthe larger velocity change?

(a) car

(b) truck

(c) The velocity change is the same (in magnitude) for bothvehicles.

(d) Can’t tell without knowing the final velocity of combined mass.

A compact car and a large truck collide head on and stick together.(Neither driver is applying the brakes.) Defining the system as thecar plus the truck, which of the following are unchanged (to a verygood approximation), from the instant immediately before thecollision to the instant immediately after the collision?

(a) kinetic energy

(b) total momentum

(c) total energy

(d) (b) and (c)

(e) (a), (b), and (c)

(Your answer may be different if you compare the situation severalminutes after the collision with that just before the collision.)

Two 1-kg carts are about to collide on a frictionless surface; one isinitially at rest, the other comes in at a speed of 4 m/s. From theinformation given, you

(a) can

(b) cannot

determine the final velocities of the two carts.

A sandwich is placed in a sealed metal container filled with oxygengas. The metal container is immersed in a large vat of water,which is thermally insulated on all sides so that no heat canescape. A tiny spark ignites the oxygen, with the result that thesandwich is fully combusted. I measure the temperature of theknown quantity of water before and after combusting thesandwich. Which of the following is a closed system? (And whatwould be the purpose of this sort of a set-up?)

(A) Sandwich alone.

(B) All contents of metal container.

(C) Metal container + its contents.

(D) Water alone.

(E) Sandwich + water. (Use white.)

(F) Sandwich + oxygen. (Use

A

.)

(G) None of the above. (Use

B

.)

(We’ll have to improvise, because your 4-color cards only go up to“E.” I’ll try making some 8-color cards!)

A battery-powered car, with bald tires, sits on a sheet of ice.Friction between the bald tires and the ice is negligible. The driversteps on the accelerator, but the wheels just spin (frictionlessly) onthe ice without moving the car. Is the car an isolated system(considering only the coordinate along the car’s axis) — i.e. doesnothing outside the system push/pull on anything inside thesystem? Is it a closed system (i.e. negligible energy is transferredin/out of the system)?

(A) Closed but not isolated.

(B) Isolated but not closed.

(C) Both closed and isolated.

(D) Neither closed nor isolated.

A battery-powered Aston Martin car, with James-Bond-like spikedtires, sits on a sheet of ice. Agent 007 steps on the pedal, and thecar accelerates forward. Is the car an isolated system (consideringonly the coordinate along the car’s axis), i.e. nothing outside thesystem pushes/pulls on anything inside the system? Is it a closedsystem (i.e. negligible energy is transferred in/out of the system)?

(A) Closed but not isolated.

(B) Isolated but not closed.

(C) Both closed and isolated.

(D) Neither closed nor isolated.

A battery-powered Aston Martin car, with James-Bond-like spikedtires, sits on a sheet of ice. Agent 007 steps on the accelerator,and the car accelerates forward. All the while, a high-tech solarpanel on the car’s roof rapidly charges the car’s battery. Is the caran isolated system (considering only the coordinate along the car’saxis), i.e. nothing outside the system pushes/pulls on anythinginside the system? Is it a closed system (i.e. negligible energy istransferred in/out of the system)?

(A) Closed but not isolated.

(B) Isolated but not closed.

(C) Both closed and isolated.

(D) Neither closed nor isolated.

A battery-powered Aston Martin, with James-Bond-like spikedtires, sits atop an iceberg that floats in the North Sea. Agent 007steps on the accelerator, and the car accelerates forward. (Whathappens to the iceberg?) All the while, a high-tech solar panel onthe car’s roof rapidly charges the car’s battery. Which statement istrue?

(A) “Car alone” system is isolated but not closed.

(B) “Car + iceberg” system is isolated but not closed.

(C) “Iceberg alone” system is isolated but not closed.

(D) “Car alone” system is isolated and closed.

(E) “Car + iceberg” system is isolated and closed. (Use white.)

(F) “Iceberg alone” system is isolated and closed. (Use

A

.)

(G) None of the above. (Use

B

.)

I An isolated system has no mechanism for momentum to getin/out of the system from/to outside of the system. Thismeans nothing outside of the system can push/pull onanything inside of the system.

I This will make more sense when we discuss forces, week afternext.

I A hugely important idea in physics is that if the parts of asystem interact only with each other (do not push/pull onanything outside of the system), then the total momemtum ofthat system does not change.

I A closed system has no mechanism for energy to get in/outof the system. Examples so far are contrived, but soon we willlearn to calculate energy stored in springs, energy stored bygravity, etc. The concept of closed system is much moreuseful once we learn how to account for the many ways energycan be stored.

I Accounting for movement of energy in/out of a system willmake more sense when we discuss work, just after forces.

I put two carts on a low-friction track, with a compressed springbetween them. I release the spring by remote control, which setsthe carts moving apart. What system is isolated?

(A) One cart.

(B) One cart plus the spring.

(C) Cart + spring + other cart.

(D) None of the above.

I put two carts on a low-friction track, with a compressed springbetween them. I release the spring by remote control, which setsthe carts moving apart. Is the cart + spring + other cart systemclosed?

(A) Yes, for all practical purposes, because the system’s totalenergy K1 + K2 + Espring is the same before and afterreleasing the spring, and other tiny transfers of energy(escaping sound, etc.) are negligible by comparison.

(B) No.

I put two carts on a low-friction track, with a compressed springbetween them. I release the spring by remote control, which setsthe carts moving apart. Is the spring alone a closed system?

(A) Yes.

(B) No, because it transferred energy to the carts, which areoutside of what you’re now calling “the system.”

I put two carts on a low-friction track, with a lighted firecrackerbetween them. The firecracker explodes, which sets the cartsmoving apart. Is the cart + firecracker + other cart system closed?

(A) Yes, by analogy with the cart + spring + cart system.

(B) Yes, for some other reason.

(C) No, because realistically, some of the firecracker’s energy willescape in the form of heat, flying debris, etc. So really energyconservation only provides an upper limit on K1 + K2 after theexplosion, because accounting for where the energy goes ismore difficult here than for a simple spring.

(D) No, for some other reason.

(E) I still don’t understand what “closed” means.

When we collide (on a low-friction track) two carts whose massesand initial velocities are known, conservation of momentum allowsus to write

m1v1x ,i + m2v2x ,i = m1v1x ,f + m2v2x ,f

We have one equation, but two unknowns. Knowing somethingabout energy gives us a second equation. Relative speed = key.

I elastic: (v1x ,f − v2x ,f ) = −(v1x ,i − v2x ,i )

I totally inelastic: (v1x ,f − v2x ,f ) = 0

I if e is given: (v1x ,f − v2x ,f ) = −e(v1x ,i − v2x ,i )

I if change in internal energy is given:

1

2m1v

21i +

1

2m2v

22i =

1

2m1v

21f +

1

2m2v

22f + ∆Einternal

(or equivalently)

K1i + K2i + Ei ,internal = K1f + K2f + Ef ,internal

(You’ll practice working with these on HW3, and in class.)

(Here’s a problem from HW3. Let’s think about it, but not solve.)

Two carts, of inertias m1 and m2, collide head-on on a low-frictiontrack. Before the collision, which is elastic, cart 1 is moving to theright at 10 m/s and cart 2 is at rest. After the collision, cart 1 ismoving to the left at 5.0 m/s. What are the speed and direction ofmotion of cart 2 after the collision? If m2 = 6.0 kg, what is thevalue of m1?

Since the two-cart system is isolated, what equation can we writedown?

Since we are told that the collision is elastic, what second equationcan we write down?

(Check: I calculate total energy to be 100 J before and after.)

A system consists of a 4.00 kg cart and a 1.00 kg cart attached toeach other by a compressed spring. Initially, the system is at reston a low-friction track. When the spring is released, an explosiveseparation occurs at the expense of the internal energy of thecompressed spring. If the change in the spring’s internal energyduring the separation is 1000 J, what is the speed of each cartright after the separation?

Since the two-cart system is isolated, what equation can we writedown?

Since the spring’s internal energy is converted into the carts’kinetic energies, we can account for the initial and final energies ofthe cart + spring + cart system and can see that this system isclosed. (No energy goes in or out of the system.) What secondequation can we write down?

Physics 8 — Friday, September 11, 2015

I http://positron.hep.upenn.edu/physics8

I Hand in HW2. Average reported time was 3.2 hours. I’ll tryto keep them roughly this length. If you’re not sufficientlychallenged, do the XC problems!

I Pick up HW3 handout (due next Friday).

I Next week, you have two more Mazur chapters to read:Chapter 6 (about relative motion, “reference frames,” etc.)and Chapter 7 (“interactions” — a conceptual prelude toforces). They are “due” Monday and Wednesday, respectively,but the due dates are flexible because of the Rosh Hashanaholiday. A couple of days late is fine, though I imagine thisweekend is easier for reading than midweek.

I As I said Weds, I think this year we’ll just forego the quizzesand instead do a larger number of homework-like problemsthat you’ll work on together in class. It’s more fun that way.