Physics 8 Friday, October 7, 2011 Please turn in HW as you come in.

Transcription

1 Physics 8 Friday, October 7, 2011 Please turn in HW as you come in. If you ve never done so, I highly recommend googling Steve Jobs Stanford for his 2005 commencement speech at Stanford.

2 HW was much more difficult than I intended I m sorry about that. I solved all of HW 4 last weekend, and my solutions contain mostly reasoning, very little algebra. So I think that you will find next week s homework much less tedious/laborious than this week s. One silver lining is that I actually learned a lot of physics by solving today s homework! I also got to meet many more of you, as roughly half of the class showed up to study in DRL 3W2 this week.

3 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 the answer depend on the initial speeds? (Hint: begin with the zero-momentum frame for clarity.) (A) For elastic collisions, both objects always carry away equal kinetic energy (B) Which object s kinetic energy increases and which decreases depends on the initial velocities which in turn depend on the frame of reference of the observer (C) The lighter particle always carries away more of the kinetic energy in an elastic collision (D) The heavier particle always carries away more of the kinetic energy in an elastic collision

4 Homework problem 12 Two objects, forming an isolated system, collide in a totally inelastic collision. After the collision, the kinetic energy of the system is zero. What was the total momentum of the system before the collision? (A) Zero. (B) Not enough information to decide.

5 Homework problem 16 When two identical objects traveling at the same speed collide head-on, both change direction. Will they both change direction in any inertial reference frame? (A) Yes. (B) No: there are some frames of reference in which one or both particles do not change direction.

6 Homework problem 17 Is the total kinetic energy of a system zero when measured from the zero-momentum frame for the system? (A) Yes. (B) No never. (C) Not necessarily.

7 Homework problem 18 You and your identical twin are on adjacent elevators in a skyscraper. Your elevator is stopped, but your sibling s elevator is descending quickly at constant speed. At the same instant, you both happen to drop your keys. Which set of keys hits the elevator floor 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 is descending.

8 Tension in cables... In the 17th century, Otto von Güricke, a physicist in Magdeburg, fitted two hollow bronze hemispheres together and removed the air from the resulting sphere with a pump. Two eight-horse teams could not pull the halves apart even though the hemispheres fell apart when air was readmitted. Suppose von Güricke had tied both teams of horses to one side and bolted the other side to a heavy tree trunk. In this case, the tension on the hemispheres would be (A) twice (B) exactly the same as (C) half what it was before.

9 Suppose a horse can pull 1000 N F A on B = F B on A F A on B = F B on A = 1000 N T = 1000 N a = 0

10 Tree stays put, no matter how hard I pull F A on tree = F tree on A F A on tree = F tree on A = 1000 N T = 1000 N a = 0

11 Tree stays put, no matter how hard I pull F A+B on tree = F tree on A+B F A+B on tree = F tree on A+B = 2000 N T = 2000 N a = 0

12 Horse C loses his footing when he pulls > 1000 N F A+B on C = F C on A+B = 2000 N T = 2000 N Force of ground on C is 1000 N to the right. Tension pulls on C 2000 N to the left. C accelerates to the left. a C = (2000 N 1000 N)/m C

13 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...

14 Bathroom scale on moving elevator A bathroom scale typically uses the compression of a spring to measure the force of Earth s gravity (F = mg) on you, which we call your weight. Suppose I am standing on such a scale while riding an elevator. With the elevator parked at the bottom floor, the scale reads 700 N. I push the button for the top floor. The door closes. The elevator begins moving upward. At the moment when I can feel that 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.

15 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 p i Chapter 8 defines force as the rate of change of momentum: F = d p p = F dt dt If you integrate an external force over time, the resulting change in momentum is called the impulse delivered by the external force: J = p = F external dt Same definition as in Chapter 4, but now you can calculate J from external forces instead of introducing it in an ad-hoc way.

16 Force vs. impulse Bridge abutments now sometimes have a row of sand-filled or water-filled plastic barrels in front of them to increase the survivability of a collision in a car that runs off the road. Which does the presence of the barrels change: (A) the impulse delivered to the car (B) the force exerted on the car (C) both (D) neither

17 Equation of motion Something on equation of motion? Was noted as a confusing part of the chapter.