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.

When a glass rod is rubbed with silk, it becomes positive and the silk becomes negative, yet both attract dust. Is it possible the dust has a third type of charge that is attracted to both positive and negative? Explain. Which model: 2 types or 3 types of charge would be a simpler model?

6. Which of the following are steps toward measuring the distance to stars using spectroscopic parallax? a) Measure the star’s spectral type and calculate the mass. b) Measure the star’s spectal type and the apparent brightness, i.e., the flux. c) Measure the star’s rotation period and the number of starspots. d) Measure the star’s orbital period if it is in a binary and use that to estimate the spectral types of both stars. e) Measure the slight wobble in the star’s motion caused by planets orbiting the star.

What single piece of information revolutionized our understanding of “spiral nebulae”, such as the spiral nebula in Andromeda, to show that they are spiral galaxies full of stars? a) We measured their average temperature. b) We placed them on the Hertzsprung-Russel diagram. c) We measured their distance. d) We measured their parallax. e) We measured their orbital periods

2. Which statement about our Galaxy, the Milky Way, is true? a) The halo contains no O and B stars while the disk contains stars of all spectral types. b) The halo contains only young stars while the disk contains stars of all ages. c) The halo contains hundreds or perhaps thousands of “super-massive” black holes. d) Our Sun is located a few light years from the center of our Galaxy. e) The Milky Way is unique in having no smaller galaxies orbiting around it.

A thin wall cubic container is half-filled with water. What is the vertical position of the center of gravity if the container is tipped over just to the point where is about to spill water? Consider the side of the cube d = 0.30 m.

a. y_CG = 0.14 m

b. y_CG = 0.21 m

c. y_CG = 0.23 m

d. y_CG = 0.25 m

Cosmic microwave background

Q: How is the CMB cosmic? Microwave? Background? Radiation?

Q: What are observed CMB properties?

Q: What is the last scattering surface?

Q: How does CMB verify the Cosmological Principle?

Q: What are the three possibilities for the cosmic geometry? How does CMB tell us about the geometry of the universe?

The New England Merchants Bank Building in Boston is 152 mm high. On windy days it sways with a frequency of 0.19 HzHz , and the acceleration of the top of the building can reach 1.5 %% of the free-fall acceleration, enough to cause discomfort for occupants.

What is the total distance, side to side, that the top of the building moves during such an oscillation?

List 4 things we can learn about a star using spectroscopy.

Suppose you have 2.0mol of O2 gas.

How many coulombs of positive charge are contained in this gas in the atomic nuclei?

Express your answer using two significant figures