[13 marks]

(a) An object is subjected to the force F = 4x⁴ z ı ^ + 4 z^{3k ^} N, where x and z are in metres. The object can only move in the xz-plane.

          (i) The object moves from the origin by moving first along the x-axis to (a, 0) and then parallel to the z-axis to the point with coordinates (a,b). How much work does the force do?

          (ii) The object moves from the origin by moving first along the z-axis to (0,b) and then parallel to the x-axis to the point with coordinates (a,b). How much work does the force do?

          (iii) Is this a conservative force?

          (iv) Can this force be expressed as the gradient of a potential? If so, give an expression for the potential. If not, give reasons why.

Q1 We have naturally occurring radioactive material with the chemical formula (Ce,La,Nd,Th)(PO4,SiO4). A sample of the ore is mined and is concentrated to 5%, 10%, 25% and 100% monazite So four samples are created in 5%, 10%, 25% and 100% of this monazite.

a. Calculate the activity of the samples. Thorium 232 with a known half life in literature should be used in activity calculations.

b. would activity be different if the samples with 10% and 25% were dissolved in acids or other minerals? assume same percentages.

show all steps for the question to be worth any marks the result should be given in Bq/gram thorium 232 half life is public information and it should be used in this case.

Question 7: Cosmology

a. Write 2 – 3 sentences identifying and describing the most widely accepted scientific theory for the formation of the universe.

b. Write 2 – 3 sentences explaining redshift and what it led scientists to conclude about the universe.

c. Scientists have proposed three models of the universe that describe three different futures for the universe. Write 2 – 3 sentences comparing the future of the universe according to the closed and open models.

As part of previous adventures, formerly conjoined identical twin, Sue, is now 13.4 years younger than her identical twin Lou. (The anniversaries of their birth are no longer the same day.) It is Lou's turn to travel at least 0.9c. During his round trip, Lou ages 1 year. When he returns, Lou and Sue once again turn their next respective age on the same day.

a) How much does Sue age while Lou is on his trip? (There is more than one possible answer.)

b) How fast does Lou travel (from Sue's point of view)?

Two brass rods AB and BC, each of uniform diameter, will be brazed together at B to form a nonuniform rod of total length L=110 m that will be suspended from a support at A as shown. Knowing that the density of brass is ρ=9000 kg/m3 and the diameter of AB is c=16 mm, Determine (a) the length of rod AB for which the maximum normal stress in ABC is minimum, (b) the corresponding value of the maximum normal stress.

https://media.cheggcdn.com/study/bc1/bc172d89-4cc0-4d54-b938-583fbc0d8e1e/4739-1-6IP1.png

a.The maximum axial stress, in member AB, is written as max(σ_AB)=(   a+   ) (MPa)

b.The maximum axial stress, in member BC, is written as max(σ_BC)= (   -   a) (MPa)

A thin, horizontal 11cm×11cm11cm×11cm copper plate is charged with 1.7×10¹⁰ electrons. Consider the electrons are uniformly distributed on the surface.

Part A

What is the strength of the electric field 0.1 mmmm above the center of the top surface of the plate?

Express your answer using two significant figures.

Part B

What is the direction of the electric field 0.1 mmmm above the center of the top surface of the plate?

What is the direction of the electric field 0.1 above the center of the top surface of the plate?

How was the Big Bang different from an ordinary explosion? Where in the universe did it occur?

A brass plug is to be placed in a ring made of iron. At 20 ∘C∘C, the diameter of the plug is 8.754 cmcm and that of the inside of the ring is 8.739 cmcm .

1.They must both be brought to what common temperature in order to fit?

Express your answer using two significant figures.

2.

What if the plug were iron and the ring brass?

Express your answer using two significant figures.

Consider an infinitely long, straight coaxial cable consisting of a homogeneous cylindrical center conductor with radius a and a surrounding conductive tube (shield) with inner radius b.

The space between the center conductor and the screen is filled with a dielectric with e_r (epsilon r) = 1. In the inner conductor, a direct current I is distributed evenly over the cross section. In the outer conductor there is a corresponding return current. On the surface of the inner conductor there is a constant surface charge density Ρ_s,1 which determines how the power is transported in the cable.

(On the inside of the screen there is a corresponding constant surface charge density Ρ_s,2= -a / b * P_{s, 1})

Determine the Poynting vector S = E x H for the cable.

Neglect the center conductor and the screen resistivities.
Tip: Calculate S and H in '' Normal '' way.

Please solve a Laplacian in spherical form with complete details?

a) Determine the amount of heat per gram which must be removed to convert 110 OC steam (H2O(g)) into –10 OC ice(H2O(s)), then find the total heat removed if there is 9.50 g of steam.

b) For acetic acid (CH3COOH, with one O bonded to an H), acetone (CH3COCH3, with the O bonded only to a C), and carbon tetrachloride (CCl4, see non polar molecules in section 12.10), determine the predominant types of intermolecular attraction for the pure liquids, and predict whether the vapor pressures, boiling points, viscosity, and surface tensions will be low or high.

c)For tantalum (Ta), calcium chloride (CaCl2), fructose (C6H12O6), and diamond (C), determine the type of solid and describe the expected physical properties.

As you observe a standing wave on a string (e.g. with a strobe light), you notice certain times when the string is completely flat. What has happened to the energy stored in the wave at those instants? b) Are there any instants when the velocity of every portion of the string is simultaneously zero? What does it look like? Draw a picture and explain your answer.

1. (20pts) Design a 3-bit counter that counts from 0000 to 1111 using JK flip/flops. Do not forget to include the carry to detect overflow.

Are Maxwell's equations symmetric?

What is the magnetic monopoly problem?

How are magnetic monopoles found?

Explain by reference.

2. The Hungry Tuna

What is the minimum number of fish a 3m long bluefin tuna would have to eat to fuel a non–stop voyage across the Atlantic in two weeks if they traveled at 14.88 km/hr on average? How often would prey fish need to be captured during this voyage? Assume a travel distance of 5000 km and that the tuna can extract 1000 kJ of energy from each prey fish. You may also assume that the body is elliptical in cross–section, that the body height is 1/4 the body length and the body width is 1/8 the body length.

Edit: The mass of the tuna is not given. This problem is solvable with the information given above.

.

Answer: The tuna must eat at least 57 fish. Given that this occurs over 2 weeks, the tuna must eat at least 4.05 fish each day. But how do I get to this answer? Please show work and formulas used to get the provided answers. Thank you!