even though a Jovian planet is close to its star, its interior temperature is cool. explain what this tells me about the planet's mass.

On the exoplanet Trappist-1d, g = 6.74 m/s² and on Mars g = 3.73 m/s². A fully suited-up astronaut has a mass of 125. kg.

1) When she is on a ladder 1.50 m above the surface of Mars she has more potential energy, PE, than when 1.50 m above Trappist-1d's surface. True or False

2) At 1.50 m above the Mars surface, her PE in units of J is: A) 125, B) 188, C) 699, or D) 1.84 x 10³

3) If she falls off the ladder on Mars, her final speed just before landing depends on her mass. True or False

4) What is her speed just before landing on the surface of Mars? (in m/s)

5) Your above answer for the speed assumed that there was no net non-conservative work. That is, W_nc = 0. True or False

6) If net non-conservative work is done on an object, its total mechanical energy (KE + PE) changes with time and W_nc = ΔKE + ΔPE = E^tot(final) - E^tot(initial)

7) A high-tech boat (m_b = 900. kg) with a criminal villain (m_c = 100. kg) onboard is drifting with a speed of 1.30 m/s under a bridge when a 300. kg super-hero jumps straight down from the bridge. After the hero lands on the boat, what is the speed in m/s of the boat? (Assume that the system of boat, villain and super hero is isolated.)

A) -0.500, B) - 0.300, C) 0, D) + 0.300, E) +1.00, or F) +1.30

9) You are in a canoe which is initially at rest on a frictionless lake. You then move forward (positive direction) in the canoe.

As a result of your motion, the momentum of the canoe becomes negative. True or False

In a thought experiment, a cubic box of side length 0.01 mm contains three particles. One particle moves just in the x-direction, colliding elastically with the left and right walls of the cube. The second atom moves just in the y-direction, colliding elastically with the front and back walls of the cube. The third atom moves just in the z-direction, colliding elastically with the top and bottom walls of the cube. All three atoms have speed 500 m/s and mass 6.7x10-27 kg. What is the average pressure in the box?

A. 1.7 × 10-3 Pa

B. 1.7 × 10-6 Pa

C. 3.3 × 10-3 Pa

D. 5.0 × 10-6 Pa

E. 1.01 × 10-5 Pa

F. 3.10 x 10-5 Pa

1. A commuter train passes a passenger platform at a constant speed of 41.7 m/s. The train horn is sounded at its characteristic frequency of 350 Hz.

(a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (Indicate whether the frequency increases of decreases with the sign of your answer.)
(b) What wavelength is detected by a person on the platform as the train approaches?

2. Two small speakers are driven by a common oscillator at 8.55 ✕ 10² Hz. The speakers face each other and are separated by d = 1.23 m.

Locate the points along a line joining the two speakers where relative minima would be expected. (Use v = 343 m/s. Choose one speaker as a reference and enter your answers as positive distances from this speaker, from smallest to largest. There are 6 boxes. Enter NONE in unused answer boxes.) Unit in m.

Why is a diffraction grating better than a two-slit setup for measuring wavelengths of light?

given an electron has orbital angular momentum and spin angular momentum, l and s respectively.

given the following relations:

[lx,ly] = ih(bar)lz , [ly,lz] = ih(bar)lx , [lz,lx] = ih(bar)ly

[sx,sy]= ih(bar) sz , [sy,sz] = ih(bar)sx , [sz, sy\ = ih(bar)sy

(a) prove first that for an arbitary operator A, B that AB=BA+[A,B]

(b) show that [lx,l^2] = 0 where l^2 = l*l = lx^2 + ly^2 + lz^2

(c) show that similarly, [ly,l^2]=0 and [lz,l^2]=0

(d)given that the total angular momentum operator, j, is defined as j=l+s show that

j^2 = jx^2 +jy^2 +jz^2 = l^2 + s^2 + 2l*s

if l*s = lxsx + lysy + lzsz

(e) show that it is also possible to find the simultaneous eigenfunction of j^2 and jz (show as much work as possible)

(f) is it then possible to determine simultanesou eigenfunction of j^2, jz and l^2? (show as much work as possible)

***Please answer ALL parts, not just a few of them***

*** most important parts that I am confused on is part e and f***

Assignment – The World’s Largest Ferris Wheels
The Singapore Flyer is a giant Ferris wheel located in Singapore. Described by its
operators as an observation wheel, it reaches 42 stories high, with a total height of 165 m,
making it the tallest Ferris wheel in the world. Situated on the southeast tip of the
Marina Centrereclaimed land, it comprises a 150 m diameter wheel, built over a three-
story terminal building which houses shops, bars and restaurants. Each of the 28 air-
conditioned capsules is capable of holding 28 passengers, and a complete rotation of the
wheel takes about 30 minutes.
The Star of Nanchang is a 160-metre tall giant Ferris wheel located in the eastern Chinese
city of Nanchang, the capital of Jiangxi Province. A single rotation takes approximately 30
minutes; the slow rotation speed allows passengers to embark and disembark without the
wheel having to stop turning.( the diameter is 153)
The 190.5 m New York Wheel is going to be constructed at Staten Island, New York
Cityalong with the Harbor Commons retail complex.A single ride will last about 38 minutes.
The construction began in May 2015, withthe gaol of opening the attraction by April 2018.(
the diameter is 183)
Your Task
1. Calculate the speed of these three Ferris wheels in metres/minute. ( 6 marks)
2. Design a Ferris wheel of your own, with a diameter somewhere between 160 m and
190.5 m. Your Ferris wheel should be faster than the slowest of those above, but
not as fast as the fastest.Use mathematics to justify that your Ferris wheel meets
these specifications.
3. Draw a scale diagram of your Ferris wheels. ( 1 mark)
4. On the same coordinate system, draw two curves modelling the height of a
passenger with respect to time for 1 of the three and your wheels. Draw at least
two cycles for each Ferris wheel. Start each cycle at the height where the
passenger gets on the wheel. (Hint: Determine the period, amplitude, and equation
of the axis for each graph.)

A 31 kg crate full of fruits is placed on an incline that is 17◦ below the horizontal. The crate is connected to a spring that is anchored to a vertical wall, such that the spring is parallel to the surface of the incline.

(a) If the crate was connected to the spring at equilibrium length, and then allowed to stretch the spring until the crate comes to rest, determine the spring constant. Assume that the incline is frictionless and that the change in length of the spring is 2.13 m.

(b) If there is friction between the incline and the crate, would the spring stretch more, or less than if the incline is frictionless? You must use concepts pertaining to work and energy.

Show a complete solution to the following question.
A 10.0 kg block is being held in place at the top of a rough ramp which is at a 45 o angle to the horizontal. The coefficient
of static friction between the ramp and the block is 0.15 and the coefficient of kinetic friction is 0.10. There is a spring at
the bottom of the ramp lying parallel to the ramp and it obeys Hooke’s Law. The spring constant is 1200 M/m. The
distance between the side of the block facing the spring and the upper surface of the spring is 3.0 metres.

(a) Make an FBD for the block when it is sliding down the ramp.
(b) Calculate the speed of the block just before it makes contact with the spring.
(c) Set up the equation which would determine the maximum compression of the spring after the block makes contact with
the spring. You DO NOT have to solve the equation but you do need to clearly define any variables which appear in the
equation.

You are in a circular Earth orbit with a velocity of 1 DU/TU. Your service module is in another circular orbit with a velocity of 0.5 DU/TU. What is the minimum delta v needed to transfer to the service module's orbit ? (Answer: 0.449 DU/TU).

Some virtual teams at Boeing have discussions focused on military aircraft. Do some Internet research on UC security mechanisms and identify and briefly describe several that Boeing should have in place to ensure the privacy and integrity of such discussions.

I need the answer with no plagarism.

Calculate the reactive force and reactive muscle moment at Justin Verlander’s knee for a seated leg extension, with a weight of 55, 75, and 95 lbs. Assume that the leg is held at an angle ??, and if it were fully extended, then ??=0. Assume that the load is applied in a way such that it remains perpendicular to the lower leg. Justin Verlander is 1.96 meters tall and has a mass of 102 kg. (Note the units!) a. State ALL of your assumptions. b. Calculate the force and reactive muscle moments in terms of ??. c. Solve for the force and reactive moments for each load at ?? = 90̊, 60̊, 30̊, 0̊.

General Relativity

Q: What is Einstein’s equivalence principle?

Q: What is gravitational lensing? Why is it useful for cosmology?

Q: What is gravitational time dilation?

Q: What are MACHOs? What does the MACHO microlensing result mean for dark matter in the Milky Way?

Q: What is the bullet cluster? How does it give evidence for dark matter and against modified gravity?

It’s early fall and you are driving along a two-lane highway in a rented moving van. It’s full of all of your possessions so you and the loaded truck weigh 8000 lb. You have just slowed down to 15 mph because you’re in a school zone. It’s a good thing you thought to do that because a group of first graders are just starting to cross the road. Just as you pass the children you see a 2000-lb sports car in the other lane heading straight for the children at about 80 mph. A desperate thought crosses your mind. You just have time to swing into the other lane and speed up a bit before making a head-on collision with the sports car. You want your truck and the sports car to crumple into a heap that sticks together and doesn’t move. Can you save the children or is this just a suicidal act?

A. Prediction: How fast would you have to be going to completely stop the sports car? Explain the reasons for your prediction. (doesn't have to be an exact answer)

B. : What happens when the less massive car is moving much faster than the more massive car? Much slower? At an intermediate speed?

C. Based on your prediction and your observations, what mathematical definition might you use to describe the momentum you would need to stop an oncoming vehicle traveling with a known mass and velocity? Should it depend on the mass, the velocity, or both? Explain your choice.