A curious person decides to do an experiment in their apartment building. They take their bathroom scale into the elevator on the 15th floor of the highrise they live in. When the elevator is stationary, they step on the scale and it reads 532 N, as expected since this is the person's weight. When the elevator starts moving, the person looks at the scale and it reads 420 N. The combined mass of the person and the elevator is 795 kg.

(a) Explain why the reading on the scale is less than the person's weight.

(b) What is the elevator's acceleration (magnitude and direction) when the scale reads 420 N.

(c) In the next part of the experiment, the person chooses a different floor to travel to and then the scale reads 670 N. Did the person choose to go to a higher floor or a lower one? And what is the acceleration of the elevator?

(d) Using the calculations you made in parts (b) and (c), find the tension in the elevator cable when the scale read 420 N and 670 N.

(e) At one point during the experiment, the person looks at the scale and it reads 0 N. Explain how this is possible and what the person should do about it.

Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Calculate the chi-square test statisticΛ20 to test the claim that the probabilities of winning are the same in the different positions. Use a= 0.05. The results are based on 240 wins.

A)Hypothesis

Ho :

Ha :

B) Critical Values= and decision to reject or fail to reject Ho

C) Conclusion about the problem statement.

The probability that electron will be found is highest when r = 0. Does this mean that electron should collapse into the nucleus? Refute this idea.

(THERMODYNAMICS) A vertical cylinder fitted with a frictionless piston contains 1.5 kg of H2O initially at 100 °C, 400 kPa.  If the volume of the system reaches 0.5 m3, the piston hits a set of stops and is restrained from further upward travel. The system is heated to 200 C. (Use saturated water tables, steam tables, and superheated tables as necessary)

a)   If the piston reaches the stops, determine the temperature and pressure when the piston first touches but exerts no force on the stops.  If the piston doesn’t reach the stops, find the final volume.  Clearly show how you determined whether or not the piston reaches the stops.

b)   Calculate the heat and work for the entire process.

c)   Show the entire process on a T-v and P-v diagram including the saturation curve.

Use at least 50000 simulations to answer the following questions.

In the game of craps, the shooter rolls two dice and wins if the sum of the dice is 7 or 11 ("natural"); he loses if the sum is 2,3, or 12 (craps). If the sum is 4, 5, 6, 8, 9, or 10, then the result is not yet decided. He must roll the dice again and again, as often as is necessary until the initial sum, be it 4, 5,6,8,9, or 10 is repeated (shooter wins) or until the sum is 7 (shooter loses). Find the probability that the shooter will win in a game of craps by simulation.

Wins   Rushing
10   2205
11   2096
11   1847
13   1903
10   1457
11   1848
10   1564
11   1821
4   2577
2   2476
7   1984
10   1917
9   1761
9   1709
6   1901
5   2288
5   2072
5   2861
6   2411
4   2289
3   2203
3   2592
4   2053
10   1979
6   2048
8   1786
2   2876
0   2560

1.What proportion of the variation in number of wins is explained by the opponent's rushing yards? Express your answer as a proportion (between 0 and 1) written to 3 decimal places.

2.What is the sample correlation coefficient r? Write your answer to 3 decimal places.

3.What is the slope for the line of best fit? Write your answer to three decimal places.

4.What is the y-intercept for the line of best fit, written to two decimal places? (Here it is technically the wins-intercept.)

5.Predict the number of wins for a team if the opponent's total rushing yards were 1800 yards. Round your answer to the nearest whole number.

An photon with a wavelength in the X-ray region of 0.69 nm undergoes Compton scattering by colliding with a free electron. 1) Assume the photon just barely grases the electron, so that the deflect angle, θ, can be considered zero.

1)What is the wavelength of the outgoing photon after the collision? λ' =

2)What the energy of the outgoing photon? E_γ =

3)Now assume the photon deflects off at a small angle of 49^o. What is the wavelength of the outgoing photon after the collision in this situation? λ^' =

4)What the energy of the outgoing photon? E_γ =

5)Next assume the photon deflects off at a larger angle of 106^o. What is the wavelength of the outgoing photon after the collision in this situation? λ^' =

6)What the energy of the outgoing photon? E_γ =

7)Finally, lets say the photon hits the electron straight on so that it deflects straight back. What is the wavelength of the outgoing photon after the collision in this final situation?λ^' = 3 here

8)What the energy of the outgoing photon?   E_γ =

10)At this point, you might want to ask yourself how your answer to part (9) compares with collisions you experience in your everyday life. For example, so the size of a ping-pong ball change depending the angle in reflects off the table? What does this tell us about a photon? One last calculation. Now, instead of scattering off of an electron, let's say the photon scatters off a proton with such an angle that is produces the maximum possible change in wavelength for this collision. What is the maximum wavelength of the outgoing photon after the collision with a proton? λ^' =

N players are bidding on an object in a first price auction. The object has a value of v_i for each player i, where v₁ > v₂> ... >v_n> 0. Each player bids secretly choosing nonnegative real number. The winner is the player who bids the largest number, and that player must pay the amount they bid. If it tie, then the player with the lowest index wins. Formulate this situation as a strategic game( describe the players, actions, and payoff functions) and show that in all the Nash equilibrium, player 1 wins the auction.