Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 11 m long, and that the cords stretch in the jump an additional 23 m for a jumper whose mass is 140 kg, the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground). (a) It will help you a great deal in your analysis to make a series of 5 simple diagrams, like a comic strip, showing the platform, the jumper, and the two cords at the following times in the fall and the rebound: 1 while cords are slack (shown here as an example to get you started) 2 when the two cords are just starting to stretch 3 when the two cords are half stretched 4 when the two cords are fully stretched 5 when the two cords are again half stretched, on the way up On each diagram, draw and label vectors representing the forces acting on the jumper, and the jumper's velocity. Make the relative lengths of the vectors reflect their relative magnitudes. (b) At what instant is there the greatest tension in the cords? (How do you know?) When the person has fallen 11 m. At the bottom, when the person has fallen 34 m. When the person has fallen between 0 m and 11 m. When the person has fallen between 11 m and the bottom. At the top, when the person has fallen 0 m. (c) What is the jumper's speed at this instant, when the tension is greatest in the cords? m/s (d) Is the jumper's momentum changing at this instant or not? (That is, is nonzero or zero?) (e) Which of the following statements is a valid basis for answering part (d) correctly? Since the momentum is zero, the momentum isn't changing. If the momentum weren't changing, the momentum would remain zero forever. After a very short time the momentum will be upward (and nonzero). Since the net force must be zero when the momentum is zero, and since is equal to the net force, must be zero. A very short time ago the momentum was downward (and nonzero). The number of significant digits is set to 3; the tolerance is +/-2% (f) Focus on this instant of greatest tension and, starting from a fundamental principle, determine the spring stiffness for each of the two cords. N/m (g) What is the maximum tension that each one of the two cords must support without breaking? (This tells you what kind of cords you need to buy.) N (h) What is the maximum acceleration (in "g's") that the jumper experiences? (Note that | if is small compared to .) g's (acceleration in m/s2 divided by 9.8 m/s2) (i) What is the direction of this maximum acceleration? (j) What approximations or simplifying assumptions did you have to make in your analysis which might not be adequately valid? (Don't check any approximations or simplifying assumptions which in fact have negligible effects on your numerical results.) Assume that the gravitational force hardly changes from the top of the jump to the bottom. Neglect air resistance, despite fairly high speeds. Assume the speeds are very small compared to the speed of light. Assume tension in cord proportional to stretch, even for the very large stretch occurring here.

There is a circle with a smaller circle inside of it. What's the electric field for the hollow sphere, with an inside radius 'a' and outside radius 'b?'

1. r > b

2. r = b

3. a < r < b

4. r = a

5. r < a

The space between a and b is filled with dense material rho.

STEP 1: Get 2 sheets of 8½ by 11 paper and 2 sheets of aluminum foil. You will need to cut the aluminum foil so that both sheets are 8½ by 11.

STEP 2: Ball up one of the sheets of paper and one of the sheets of aluminum foil.

STEP 3: Take the remaining sheet of paper and fold it in half twice so that instead of being 8½ by 11 it is 4¼ by 5½ (roughly, it doesnt have to be exact). Then do the same with the remaining sheet of aluminum foil. In the end, the folded sheet of paper and the folded sheet of aluminum foil should be roughly the same size.

STEP 4 You now have four objects (2 balled & 2 folded). You will now conduct races between the objects in the following manner. Take two of the objects, hold them at the same height (at least shoulder level) and drop them simultaneously. Observe which one strikes the ground first. It should be obvious which one strikes the ground first. If it is not then the race is a tie. You should conduct each race multiple times to verify your results. Part A Perform the following races and then enter the winner of the race in the space provided. For example, in the first race, if the balled paper wins, then type 1. If the folded paper wins, then type 2. If it is a tie, then type 3. Your answers to Part B will be based on the results of your races.

1. Race 1 (1) balled paper vs. (2) folded paper

Race 2 (1) balled paper vs. (2) folded aluminum foil

Race 3 (1) balled aluminum foil vs. (2) folded paper

Race 4 (1) balled aluminum foil vs. (2) folded aluminum foil

Race 5 (1) folded paper vs. (2) folded aluminum foil

6. Race 6 (1) balled paper vs. (2) balled aluminum foil

Part B Based on the results of your races from Part A, answer the following questions.

7. Identify the trend for the first 4 races.

The balled object always won.

The paper object always beat the foiled object.

The folded object always won.

The foiled object always beat the paper object. It was always a tie.

8. Which one of the following statements best explains the trend you observed in the first 4 races?

The two objects had no significant differences between them.

Gravity pulled harder on the winning object than it did on the other object.

The winning object had a significantly smaller surface area than the other object.

The winning object was significantly heavier than the other object.

Although one object was significantly heavier, the other object had a significantly smaller surface area. These two differences canceled each other out.

9. Which one of the following statements best explains the results of Race 5?

Since they both had roughly the same weight, surface area, & shape, the race was a tie.

Since they both had roughly the same surface area & shape, most likely the winning object had significantly more weight and thus had a higher terminal velocity.

The material the winning object is made from cuts through the air significantly better than the material the other object is made from.

The race was a tie because in the absence of air drag all objects will fall with the same acceleration.

It is impossible to explain the results.

10. Which one of the following statements best explains the results of Race 6?

Since they both had roughly the same weight, surface area, & shape, the race was a tie.

Since they both had roughly the same surface area & shape, most likely the winning object had significantly more weight and thus had a higher terminal velocity.

The material the winning object is made from cuts through the air significantly better than the material the other object is made from.

The race was a tie because in the absence of air drag all objects will fall with the same acceleration.

It is impossible to explain the results.

Draw a circuit with a battery of 90 V is connected to four resistors, R1 =10 Ω, R2,= 20 Ω , R3 =30 Ω and R4= 40 Ω, as follows. Resistors R1 and R2 are connected in parallel with each other, resistors R3 and R4 are connected in parallel with each other, and both parallel sets of resistors are connected in series with each other across the battery. (20 Points)

a. Find the equivalent resistor R12, for the partial circuits R1 and R2,

b. Find the equivalent resistor R34, for the partial circuits R3 and R4,

c. Find the equivalent resistor R1234, for the entire circuits with all four resistors R1, R2, R3, and R4

d. Find the current in the circuit with the single equivalent resistor R1234

e. Find the find the current and voltages across each of the partial circuits with resistors R12,

and R34.

e. Find the current and voltage across each of the four resistors R1, R2, R3, and R4

f. Find the power dissipated in each of the resistors R1, R2, R3, and R4

A gas expands from point A to B. The expansion consists of two stages.

Stage 1) The gas expands at constant pressure from 15 to 39 litres.

Stage 2) The gas expands from 31 litres to 82 litres with a pressure drop according to the equation; P = 100 - 0.8 V kPa

Calculate the work done on the gas.

Chapter 6:

What is electric and magnetic force?
What is the application for electric and magnetic force?
What is electric current and how digital devices work?
How do we store electrical energy?
How microphone works?
How MRI works?
Why microwave can warm your food?
What is an Electric motor?
What is Superconductivity? How magnetic levitation works?

Chapter 7:

Types of Waves
Properties of Waves
Behaviour of Waves:
- light
- Sound
- Sound in the atmosphere
- Earthquakes waves

A 91.0-kg fullback running east with a speed of 5.20 m/s is tackled by a 95.0-kg opponent running north with a speed of 3.00 m/s.

(a) Explain why the successful tackle constitutes a perfectly inelastic collision.

(b) Calculate the velocity of the players immediately after the tackle.

(c) Determine the mechanical energy that disappears as a result of the collision.
J

(d) Account for the missing energy.

A ball is tossed vertically upward from a window, height 50.0 m above the ground. The initial speed of the ball is 25.0 m/s. The ball goes up and comes down, landing on the ground at the base of the building. Determine the following:

a) The time it took the ball to reach its maximum height above ground.

b) The maximum height above the ground.

c) The time the ball returns to its initial height.

d) The velocity of the ball at the time for part c)

e) The velocity and height of the ball above ground at time t = 6.00 s.

f) The total time that the ball is in the air.

g) The impact velocity of the ball with the ground.

A 200.0 g aluminum calorimeter contains 600.0 g of water at 20.0 °C. A 100.0 g piece of
ice is cooled to −20.0 °C and then placed in the calorimeter. Use the following specific
heats: cAl = 900.0 J Kg-1 °C-1, cwater = 4186 J Kg-1 °C-1, cice = 2.10 x 103 J Kg-1 °C-1. The
latent heat of fusion for water is LF = 333.5 x 103 J/Kg.
(a) Find the final temperature of the system, assuming no heat is transferred to
or from the system.
(b) A second piece of ice at −20.0 °C with a mass of 100.0 g is added. How
much solid ice remains in the system after the system reaches equilibrium?

Answer the situations below USING PHYSICS EXPLANATIONS

1. If a tree falls in the woods and no one is there to hear it, does it make a sound?
2. If my Grandfather clock is running slow, how do I fix it? Explain.
3. Why do different people get different results if they touched a bare wire from an electrical outlet?

There was a demonstration of the falling magnet in a simple copper tube. Explain, in detail, the physics behind why the magnet slows its descent through the tube (it does not touch the sides). In your discussion be sure to explain why the magnet doesn't come to a stop in the tube and why it does not speed up.

Part a:Why are the phases across each individual component (capacitor, resistor, inductor) what they are?

Advice:            

• Start with formula ϕ=arctan(ω0^2−ω^2/γω)

for ϕ above, and consider it at the resonant frequency. (Or, equivalently, consider the phasor diagram at resonance; the phase shift ϕ is the same as the phase of the signal in that diagram.)                

Then, figure out how the different circuit components' phases should relate to Q(t)

, and thus how they relate to ϕ

• .                

• You can also make a more physically-motivated explanation, based on an intuitive analogy to mechanical resonance and simple harmonic oscillation (where "pushing on a swing" is a good picture). This is by no means required, though.            

Part B: Why is the voltage across the resistor what it is? Why is the voltage across the inductor-capacitor combination what it is?            

Part C: Why are these not exactly what you would expect (theoretically-speaking)? (Hint: the phase of the L+C contribution may be a hint as to what we are neglecting.)            

Part D: How can the voltage amplitude across the capacitor and inductor (individually) be larger than the input voltage? Where does the energy come from?

Describe an experiment that demonstrates the existence of friction force. (assuming only knowledge of the weight force and normal force)