You just purchased a new home and decided to build your hot tub behind it. After several hours of careful work in the field, you figure out that they will need to excavate exactly 5.0m3 of soil. You go out and sub-sample representative spots in the soil as it is excavated and find that it weighed 120g right after you pulled it out of the hole, and then weighed 92g after you dried it out in the oven. Your contractor excavates the site and informs you that exactly 9Mg of soil (as is/wet) were hauled away from your site. Based on this information, answer the following questions: (Show all work/units for full credit!)

A. What was the gravimetric water content of the soil sub-sample (rounded to nearest whole %)?

B. What was the bulk density of the soil (rounded to 2 decimal places)? (hint: use the sub-sample moisture content to calculate the dry weight of the larger mass of soil that came out of the 5.0m3 hole by cross multiplying WETsub/WETbulk X DRYsub /DRY/bulk)

C. What was the % solid space of this soil(rounded to nearest whole %)?

D. What was the % pore space of this soil?

E. What was the volumetric water % of this soil (rounded to nearest whole %)?

F. If this soil were completely saturated with water, how many Mg of wet soil would the contractor have to haul away?

G. If you could compact the soil that was hauled away to its maximum dry density (2.20 Mg/m3) how many m3 of disposal area would be required for it(rounded to 2 decimal places)?

H. What was the % air filled pore space in the intact soil as it was excavated? (hint: subtract volumetric water from total pore space for this).

Determine the reflection coefficient of the pulse amplitude under the following boundary conditions on the right end:

(1) Fixed end

(2) Loose end

A 100kg mass traveling with a velocity of 15m/s on a horizontal surface strikes a spring with a spring constant k = 5 N/m a. Find the compression of the spring required to stop the mass if the surface is frictionless b. Find the compression of the spring if the surface is rough (0.4ku=0)

A proton experiences no magnetic force if it travels in the direction of 30 degrees North of East.
It will experience 8x10^-17 N magnetic force directed downward into the ground if it travels due east at 1000 m/s.

Find the magnitude and direction of the magnetic field.

Two pucks are sliding on a frictionless tabletop. Block A (mass 4.11 kg) is moving to the East (+x direction) at 1.50 m/s. Block B (mass 4.93 kg) is moving to the North (+y direction) at 1.80 m/s. Assume the system to be both Block A and Block B. (Note: It could be useful to make a drawing of the situation.)
What is the x-component of the total momentum of the system before the collision?
What is the y-component of the total momentum of the system before the collision?
What is the x-component of the total momentum of the system after the collision?
What is the y-component of the total momentum of the system after the collision?

Four charges are at the corners of a square

centered at the origin as follows:

7 q at (?4 a,+3 a) ,

9 q at (+4 a,+3 a) ,

?5 q at (+4 a,?3 a) , and

9 q at (?4 a,?3 a) .

A fifth charge 9 q with mass m is placed at

the origin and released from rest

Draw diagrams to indicate qualitatively the position, nature, and size of the image formed by a converging lens of focal length f for the following object distances: (a) infinity, (b) greater than 2f, (c) equal to 2f, (d) between 2f and f, (e) equal to f, (f) less than f.

Please answer those questions. Those are about the magnetic force experiment.

Q1. Discuss how the Helmholtz coils creates a magnetic field and what direction it is (You will have to assume a direction of current for this part).
Q2. Discuss how the magnetic torque is created on the 100 turn coil and what it does.

You use a rope of length ℓ to tie the front of a 1500-kg truck to the rear of a 1000-kg car and then use an identical rope of length ℓ to tie the front of the car to the rear of a 500 kg trailer. Each rope will break if its tension exceeds 1200 N . You attach a strong cable to the rear of the truck and use a winch to pull it with a force of magnitude F.

a- What is the acceleration of the three-vehicle system in terms of F, where F is in N?

Express your answer in terms of F.

b- What is the maximum pulling force you can exert on the truck before a rope breaks?

Express your answer with the appropriate units.

c- If you now attach the cable to the front of the trailer and again pull the system, what is the maximum force with which you can pull it without snapping a rope?

Express your answer with the appropriate units.

1. Evaluate: (a+b)/(c-d) + 9/(a+d) when a=5, b=3, c=8, d=4

a. 6
b. 3
c. 15/2
d. 17/13

2. Solve for x: 5(x+3) = 35

a. 2
b. 7
c. 4
d. -4

3. Acid rain occurs primarily as a result of

a. operating a nuclear power plant
b. burning coal or oil containing sulfur
c. by-products created by operating an oil refinery
d. the use of Freon and other refrigerants

4. The "ozone holes" at the polar region arise from

a. technological use of ozone to create new chemical products
b. release of sulfur compounds into the air
c. conversion of ozone into oxygen by sunlight
d. release of Freon and related products into the atmosphere

5. Ozone is important primarily as a(n)

a. source of oxygen for breathing
b. absorber of the Sun's infra-red radiation
c. protection against the greenhouse effect
d. filter for ultra-violet waves

6. The "greenhouse effect" refers to

a. the absorption of carbon dioxide by plants
b. the release of oxygen by plants
c. the absorption of solar radiation by the Earth and its atmosphere and subsequent trapping of the energy
d. the use of greenhouses to increase the Earth's food supply

7. Of the following, the longest is

a. 2 mi
b. 2 km
c. 1000 m
d. 2000 ft

8. A bicycle travels 6 km in 20 min. Its average speed is

a. 0.3 km/h
b. 8 km/h
c. 18 km/h
d. 48 km/h

9. A car's speed increases from 0 m/s to 20 m/s in 10 s. Its average acceleration is

a. 20 m/s²
b. 10 m/s²
c. 2 m/s²
d. 0 m/s²

10. An object is dropped from the roof of a building. Its speed after 5 s (neglecting air resistance) is

a. 49 m/s
b. 9.8 m/s
c. 5 m/s
d. 1.96 m/s

11. After it leaves the hand, the acceleration of a stone thrown upward is

a. greater than that of a stone thrown downward
b. the same as that of a stone thrown downward
c. less than that of a stone thrown downward
d. zero as it moves up; 9.8 m/s² as it comes down

12. When an object is accelerated

a. its direction always changes
b. its speed always changes
c. a net force might not be acting on it
d. a net force must be acting on it

13. Of the following, the shortest is

a. 0.002 ft
b. 0.002 m
c. 0.02 in
d. 2 mm

14. A ball is thrown upward at a speed of 12 m/s. It will reach the top of its path in about

a. 0.6 s
b. 1.2 s
c. 1.8 s
d. 2.4 s

15. Given two objects of the same size and shape, where one is 4 times heavier than the other.
They are dropped simultaneously from a tower. Which of the following is true? (Neglect air resistance)

a. The heavy object strikes the ground before the light one
b. They strike the ground at the same time but the heavy object has greater acceleration because it has more mass
c. They strike the ground at the same time but the lighter object has the lower speed
d. They strike the ground at the same time with the same speed.

Consider a RC circuit. At time t = 0, the circuit is closed.

(a) Draw how the current behaves with time

(b) What about the power dissipated by the resistor? (also draw it as a function of t)

To work this problem, use the fact that the image formed by the first surface becomes the object for the second surface. The figure below shows a piece of glass with index of refraction n = 1.50 surrounded by air. The ends are hemispheres with radii R1 = 2.00 cm and R2 = 4.00 cm, and the centers of the hemispherical ends are separated by a distance of d = 7.48 cm. A point object is in air, a distance of p = 1.10 cm from the left end of the glass. (a) Locate the image of the object due to refraction at the two spherical surfaces.

a block slides down a frictionless inclined plane of height h=1m, making theta with the horizontal. At the bottom of the plane, the block continues to move on a flat surface with a coefficient of friction u = 0.30. How far does the mass move on the flat surface?

Wonder Woman and Superman fly to an altitude of 1590 km, carrying betwen them a chest full of jewels that they intend to put into orbit around Earth. They want to make this tempting treasure inaccessable to their evil enemies who are trying to gain possession of it, yet keep it available for themselves for future use when they retire and settle down. But perhaps the time to retire is now! They accidently drop the chest, which leaves their weary hands at rest, and discover that they are no longer capable of catching it as it falls into the Pacific Ocean. At what speed does the chest impact the surface of the water? Ignore air resistance, although in the real world it would make a world of difference. The radius and mass of Earth are 6370 km and 5.98

For each of the following problems, write up your solutions using the 4-step problem solving procedure (get started, plan, execute, evaluate) that is detailed in the problem set rubric. Please include sketches of the problem and words describing the steps, not just the math.

3. Design a current loop that, when rotated in a uniform magnetic field of strength 0.1 T, will produce an emf of ε=ε0 sinωt, where ε0 =110V and ω=120π rad/s.