Physics 8 — Friday, October 7, 2011 Please turn in HW 3 1 2 as you come in. If you’ve never done so, I highly recommend googling “Steve Jobs Stanford” for his 2005 commencement speech at Stanford.
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Physics 8 — Friday, October 7, 2011Please turn in HW 31
2 as you come in.
If you’ve never done so, I highly recommend googling “Steve JobsStanford” for his 2005 commencement speech at Stanford.
I HW 312 was much more difficult than I intended — I’m sorry
about that.
I I solved all of HW 4 last weekend, and my solutions containmostly reasoning, very little algebra. So I think that you willfind next week’s homework much less tedious/laborious thanthis week’s.
I One silver lining is that I actually learned a lot of physics bysolving today’s homework!
I I also got to meet many more of you, as roughly half of theclass showed up to study in DRL 3W2 this week.
Homework problem 3
In an elastic collision between a light object and a heavy object,which one carries away more of the kinetic energy? Does theanswer depend on the initial speeds? (Hint: begin with thezero-momentum frame for clarity.)
(A) For elastic collisions, both objects always carry away equalkinetic energy
(B) Which object’s kinetic energy increases and which decreasesdepends on the initial velocities — which in turn depend onthe frame of reference of the observer
(C) The lighter particle always carries away more of the kineticenergy in an elastic collision
(D) The heavier particle always carries away more of the kineticenergy in an elastic collision
Homework problem 12
Two objects, forming an isolated system, collide in a totallyinelastic collision. After the collision, the kinetic energy of thesystem is zero. What was the total momentum of the systembefore the collision?
(A) Zero.
(B) Not enough information to decide.
Homework problem 16
When two identical objects traveling at the same speed collidehead-on, both change direction. Will they both change direction inany inertial reference frame?
(A) Yes.
(B) No: there are some frames of reference in which one or bothparticles do not change direction.
Homework problem 17
Is the total kinetic energy of a system zero when measured fromthe zero-momentum frame for the system?
(A) Yes.
(B) No — never.
(C) Not necessarily.
Homework problem 18
You and your identical twin are on adjacent elevators in askyscraper. Your elevator is stopped, but your sibling’s elevator isdescending quickly at constant speed. At the same instant, youboth happen to drop your keys. Which set of keys hits the elevatorfloor first?
(A) My keys hit the floor first.
(B) My sibling’s keys hit the floor first.
(C) Both sets of keys hit the floor at the same time.
(D) The answer depends on how quickly my sibling’s elevator isdescending.
Tension in cables . . .
In the 17th century, Otto von Guricke, a physicist in Magdeburg,fitted two hollow bronze hemispheres together and removed the airfrom the resulting sphere with a pump. Two eight-horse teamscould not pull the halves apart even though the hemispheres fellapart when air was readmitted. Suppose von Guricke had tied bothteams of horses to one side and bolted the other side to a heavytree trunk. In this case, the tension on the hemispheres would be
(A) twice
(B) exactly the same as
(C) half
what it was before.
Suppose a horse can pull 1000 N
~FA on B = −~FB on A
|~FA on B | = |~FB on A| = 1000 N
T = 1000 N
~a = ~0
Tree stays put, no matter how hard I pull
~FA on tree = −~Ftree on A
|~FA on tree| = |~Ftree on A| = 1000 N
T = 1000 N
~a = ~0
Tree stays put, no matter how hard I pull
~FA+B on tree = −~Ftree on A+B
|~FA+B on tree| = |~Ftree on A+B | = 2000 N
T = 2000 N
~a = ~0
Horse C loses his footing when he pulls > 1000 N
|~FA+B on C| = |~FC on A+B | = 2000 N
T = 2000 N
Force of ground on C is 1000 N to the right. Tension pulls on C2000 N to the left. C accelerates to the left.
| ~aC | = (2000 N− 1000 N)/mC
Measuring your weight (F = mg) with a spring scale
Most bathroom scales work something like this:
Now suppose I take my bathroom scale on an elevator . . .
Bathroom scale on moving elevator
A bathroom scale typically uses the compression of a spring tomeasure the force of Earth’s gravity (F = mg) on you, which wecall your weight.
Suppose I am standing on such a scale while riding an elevator.With the elevator parked at the bottom floor, the scale reads700 N. I push the button for the top floor. The door closes. Theelevator begins moving upward. At the moment when I can feelthat the elevator has begun moving upward, the scale reads
(A) a value smaller than 700 N.
(B) the same value: 700 N.
(C) a value larger than 700 N.
What is impulse?
Chapter 4 defined impulse as a change in momentum caused by a(non-isolated) system’s interaction with something external:
~J = ~pf − ~pi
Chapter 8 defines force as the rate of change of momentum:
~F =d~p
dt⇔ ∆~p =
∫~F dt
If you integrate an external force over time, the resulting change inmomentum is called the impulse delivered by the external force:
~J = ∆~p =
∫~Fexternal dt
Same definition as in Chapter 4, but now you can calculate ~J fromexternal forces instead of introducing it in an ad-hoc way.
Force vs. impulse
Bridge abutments now sometimes have a row of sand-filled orwater-filled plastic barrels in front of them to increase thesurvivability of a collision in a car that runs off the road. Whichdoes the presence of the barrels change:
(A) the impulse delivered to the car
(B) the force exerted on the car
(C) both
(D) neither
Equation of motion
Something on equation of motion? Was noted as aconfusing part of the chapter.
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