Three vectors are given as A=<3.5, -5.3, 1.1> B=<4.5, 7.5, -7> C=<-3.9, 4.8, -6>

a) Determine the angle between A and B.

b) Determine the angle between A and C

c) Compute the dot product of B and C

d) Determine the size of the area associated with vectors B and C.

e) Determine the quantity (B (dot)(A(cross)C))

Two horizontal metal plates, each 10.0 cm square, are aligned 1.00 cm apart with one above the other. They are given equal-magnitude charges of opposite sign so that a uniform downward electric field of 1.96 103 N/C exists in the region between them. A particle of mass 2.00 10-16 kg and with a positive charge of 1.09 10-6 C leaves the center of the bottom negative plate with an initial speed of 1.04 105 m/s at an angle of 37.0° above the horizontal. (c) Where does it strike, relative to its starting point? (Enter the horizontal distance from the initial position.)

1 (a) Assume that the lights in your kitchen use 300 watts. How much energy and how much does it cost to leave the lights on 24 hours a day for a week if electricity is 8 cents/kilowatt hour?

(b) For a month (assume 30 days/month)?

(c) For a year?

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2 (a) How much energy and how much money do you use to run your window air conditioner rated at 1500 watts continuously for the month of July (assume 8¢/kWh)?

(b) If you assume that coal was used to produce the electricity for your air conditioner, how much coal was burned to produce the electricity used?

(c) How much CO2 was produced by the electricity used to run your air conditioner?

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3 (a) An average incandescent light bulb has a life expectancy of 1,000 hours. How much energy would a typical 60 watt bulb use in a lifetime, assuming it lasts for 1,000 hours?

(b) At 8¢/kWh, how much would it cost over its lifetime?

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4 (a) A compact fluorescent bulb uses 15 watts and has a life expectancy of 10,000 hours. How much energy and how much would it cost to use a compact fluorescent for 10,000 hours?

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5 (a) If your car gets 20 miles per gallon (MPG), and you drive an average of 10,000 miles each year, how many gallons of gas do you use a year?

(b) At $3.00 per gallon, how much will you spend on gasoline for the year?

(c) If the combustion of each gallon of gasoline produces 22 lbs of CO2, how much CO2 does your car produce each year?

(d) If you traded your car in & bought one that got 25 MPG, how much gasoline would you save in one year?

(e) How much money would you save?

(f) How much less CO2 would be emitted into the atmosphere from your improved car?

A damped oscillator has a frequency w' that is 10% less than its undamped frequency. a) By what factor is the amplitude of the oscillation decreased during each oscillation? b) By what factor is its energy reduced during each oscillation.

A 0.5530-kg ice cube at -12.40°C is placed inside a chamber of steam at 365.0°C. Later, you notice that the ice cube has completely melted into a puddle of water. If the chamber initially contained 6.790 moles of steam (water) molecules before the ice is added, calculate the final temperature of the puddle once it settled to equilibrium. (Assume the chamber walls are sufficiently flexible to allow the system to remain isobaric and consider thermal losses/gains from the chamber walls as negligible.) Use the following values for the heat capacities of ice, water and steam Ice=2093 J/(kg x C) Water=4186 J/(kg x C) Steam= 2009 J/(kg x C)

Research 4 types of technology that we have in our world that are related to either magnetism or electromagnetism. The technology can be directly related to these topics or just a snowball effect and only somewhat related to them.
Yo should include:
3 examples of technology
Explanation how the technology helps humans (or will help them in future)
Explanation how the tecnology is related to magnetism or electromagnetism

An infinite line of charge with linear density λ₁ = 7.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.2 cm and outer radius b = 4.1 cm. The insulating shell is uniformly charged with a volume density of ρ = -562 μC/m³.

1) a) What is λ₂, the linear charge density of the insulating shell?____μC/m

b) What is E_x(P), the value of the x-component of the electric field at point P, located a distance 7.9 cm along the y-axis from the line of charge?____N/C

c) What is E_y(P), the value of the y-component of the electric field at point P, located a distance 7.9 cm along the y-axis from the line of charge?___N/C

d) What is E_x(R), the value of the x-component of the electric field at point R, located a distance 1.1 cm along a line that makes an angle of 30^o with the x-axis?_____N/C

e) What is E_y(R), the value of the y-component of the electric field at point R, located a distance 1.1 cm along a line that makes an angle of 30^o with the x-axis?____N/C

f) For how many values of r: (2.2 cm < r < 4.1 cm) is the magnitude of the electric field equal to 0?

none

one

more than one

g) If we were to double λ₁ (λ₁ = 14.4 μC/m), how would E, the magnitude of the electric field at point P, change?

E would double

E would increase by more than a factor of two

E increases by less than a factor of two

E decreases by less than a factor of two

E decreases by more than a factor of two

h) In order to produce an electric field of zero at some point r > 4.1 cm, how would λ₁ have to change?

Change its sign and increase its magnitude

Change its sign and decrease its magnitude

Keep its sign the same and increase its magnitude

Keep its sign the same and decrease its magnitude

1). Indicate whether the object will remain in circular motion or not for each case below. Show a calculation as proof. If it doesn’t stay in circular motion, state what happens to it.

a). A car traveling at a speed of 24 m/s around an unbanked curve with a radius of curvature of 108 m and a coefficient of static friction of 0.36 .

b). A person riding in a roller coaster car as it goes over the top of a curve with a radius of curvature of 33 m at a speed of 16 m/s.

The Problem:

The air inside an inflatable stand-up paddle board is 68.0°F and a gauge measures the pressure of this air to be 10.0 psi. If the volume of the air inside the board is reduced by 12.0% and the temperature increases to 102.2°F, what is the final gauge pressure of this air, in psi? (1.00 psi = 0.0680 atm)

Intermediate steps:

a.) This problem requires use of the ideal gas law, which can be expressed separately for the two relevant snapshots in time. What is the ideal gas law? [Consider: Which variables will not change between the two snapshots in time, that is between the initial and final states?]

b.) Only absolute values are used in the ideal gas law: absolute temperature, absolute volume, and absolute pressure. (“Absolute” means that a zero value is a true zero temp/pressure/volume.) Convert the initial and final temperature values (68.0°F and 102.2°F, respectively) along with the initial gauge pressure (10.0 psi) into absolute temperature and absolute pressure (in atm) values. Assume the air pressure outside of the paddleboard is 1.00 atm, or “standard pressure”. [Think: What is the reading on the pressure gauge when it is not being used to make a pressure measurement?]

c.) The volume of the board is not provided, only a relationship between the initial and final volumes. State this relationship in an equation (e.g. V_final = ___ V_initial). [Check: Which volume, final or initial, is greater? Does your equation/relationship correspond?]

d.) Without entering numerical values, write an expression for the final absolute pressure. [Recommended steps: (i) Using the ideal gas law, put all values that will change (the variables) on one side of the equal sign, and all values that are constant on the other. (ii) Equate the expressions for the variables from the initial and final states, as they equal the same constant expression. (iii) Solve for the final absolute pressure.] Now, numerically solve for final absolute pressure.

The solution:

e.) What is the final gauge pressure of the air inside the paddle board, in psi? [Please enter this answer as your final value. How many significant figures should be submitted?]

An attacker at the base of a castle wall 3.85 m high throws a rock straight up with speed 8.00 m/s from a height of 1.50 m above the ground. (a) Will the rock reach the top of the wall?

Yes No    

(b) If so, what is its speed at the top? If not, what initial speed must it have to reach the top?
m/s

(c) Find the change in speed of a rock thrown straight down from the top of the wall at an initial speed of 8.00 m/s and moving between the same two points.
m/s

(d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations?

Yes No    

(e) Explain physically why it does or does not agree.

A 3.9 g aluminum foil ball with a charge of +4.6×10−9 C is suspended on a string in a uniform horizontal E⃗ field. The string deviates to the right and makes an angle of 30∘ with the vertical. Determine the magnitude of the electric field.

1) When people sleep, their metabolic rate is about 2.6 * 10^-4 C/(s*kg). How many Calories does a 81 kg person metabolize while getting a good night's sleep of 8.5 hrs?

2) To determine the specific heat of an object, a student heats it to 100 °C in boiling water. She then places the 34.5-g object in a 151-g aluminum calorimeter containing 114 g of water. The aluminum and water are initially at a temperature of 20.0 °C, and are thermally insulated from their surroundings. If the final temperature is 23.6 °C, what is the specific heat of the object?

1). Physics ). . Place a positive and negative charge on the same y value, with different x-values.How does the field behave?. Does the field ever point only in the x or y

direction? Where does that occur in relation to the point charge?.

2). Open Charges and field simulation ( https://goo.gl/fHg5tj). Once the simulation opens, check the box next to Grid and next to values.

3). Place a single positive point charge in the simulation, and use an E-field sensor ( yellow balls) to measure the magnitute and direction of the electric field. How does the field change as you move away from the charge?

4).Now place a negative charge in the grid. How does the E-field change? What is similar and different to its behavior with the positive charge?

Question-1 Briefly sketch how Bohr derived the Rydberg’s empirical formula for atomic spectra using mix of classical mechanics and some ad hoc quantum assumptions. Indicate which steps in the derivation are motivated by classical mechanics and which are the quantum assumptions.

Question-2 Compute ionization energies of H, He+ and Li++ ions (Essentially all of them are one electron atoms) from ground state. Explain the trend.