An infinitely long solid cylindrical insulator of radius 13.0 cm has a non-uniform volume charge density of =4r3 where is in Cm3 when r is in meters. Calculate the magnitude of the electric field at a distance of 17.00 cm from the axis of the cylinder.

Given two vectors a = 3.6i -3.8j and b =6.3i+8.3j

what is the magnitude (in m) of the vector a?

Find the direction (in ° = deg) of the vector a.

Find the magnitude of the vector b.

Find the direction (in °) of the vector b.

Find the magnitude of the vector a+b.  

Find the direction of the vector a+b.  

Find the magnitude of the vector b-a.  

Find the direction of the vector b-a

Find the magnitude of the vector a-b.  

Find the direction of the vector a-b

12) The amount of electrical energy stored in a system of two charged particles a distance dd apart is

UE(d)=kq1q2/d

where particle 1 has charge q1, particle 2 has charge q2, and Coulomb's constant has the value k=k= 8.99×10⁹ N m22/C22.

Suppose that you have two particles of charge q1=7q1=7 nC and q2=−7q2=−7 nC. Let's say that you hold the positively charged particle in a fixed position while you steadily move the negatively charged particle farther and farther away at a constant speed of 3 m/s. The distance between the particles therefore changes according to the usual distance formula

d(t)=di+vt,

where v is the given speed and di=3 mm is their initial separation distance.

How much power do you deliver to the system at the time t=1s as you steadily separate the particles?

A jet fighter is accelerated from rest to a takeoff speed of 262 km/h in a distance of 91.5 m on an aircraft carrier. Assume constant acceleration.

What is the acceleration of the fighter in m/s2?

Part B

How long does it take the jet to reach take-off speed?

two electrical charges, q1= -20.0 nC and q2= +10.0 nC, are located on the x-axis at x= 0 m and x= 1.00 m, respectively. What is the magnitude of the electric field at the point x= 0.50 m, y= 0.50 m?

You're considering installing a 4-foot-high by 8-foot-wide picture window in a north-facing wall (no solar gain) that now has a total R (specific thickness of material) value of 23. As a compromise between initial cost and energy savings, you've chosen a standard double-glazed window with the value of R is 2.0. As a result of installing this window, how much more oil will you burn in a 6-month winter heating season with an average outdoor temperature of 25F and an indoor temperature of 68F? Assume your oil furnace is 80% efficient.

A 5.4-µC point charge is located at x = 1.1 m, y = 2.9 m, and a -4.3-µC point charge is located at x = 2.3 m, y = -1.9 m.

(a) Find the magnitude and direction of the electric field at x = -2.7 m, y = 1.2 m.

(b) Find the magnitude and direction of the force on a proton at x = -2.7 m, y = 1.2 m.

Suppose the water at the top of Niagara Falls has a horizontal speed of 1.20 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 47.3 ° angle below the horizontal?

In one model of the hydrogen atom, an electron orbits a proton in a circle of radius 5.28×10^-11 m with a speed of 2.18×10⁶ m/s. What is the acceleration of the electron in this model?

What is the period of the motion?

Option 1 – How We Hear This activity explores how we hear and how the physical nature of the sound wave determines the quality of the sound experience. Structure of the Ear What are the three main regions of the ear and their associated parts? Briefly describe what happens inside the cochlea? Sound Waves & Frequency What are the three aspects of sound waves? Briefly describe each aspect. Which type of tuning fork would vibrate faster—a small, short one or a large, long one? How is frequency measured and calculated? Explain why longer sound waves lead to lower frequencies and why shorter sound waves lead to higher frequencies. The Theory of Sound Briefly describe the three theories relating to how we perceive pitch. Explain why no single theory can explain human perception of pitch from 20 to 20,000 Hz.

I take my dogs on an afternoon walk. We leave my house, walking due East for 4 km. We then walk 3.5 km at an angle of 35 degrees West of North. Finally, we ealk 5.4 km at an angle of 15 degrees West of South. If I were to walk along a straight path that wuld take us back to my house, how far and in what direction should I walk?

You push a small mass (with respect to your mass) crate on a frictionless surface and it has some acceleration. If you are standing on the same frictionless surface, what happens to you?

Two solid bodies at initial temperatures T1 and T2, with T1 > T2, are placed in thermal contact with each other. The bodies exchange heat only with eachother but not with the environment. The heat capacities C ≡ Q/∆T of each body are denoted C1 and C2, and are assumed to be positive.

(a) Is there any work done on the system? What is the total heat absorbed by the system? Does the internal energy of each subsystem U1 and U2 change? What about the total internal energy U = U1 + U2?

(b) Calculate the final temperature, Tf , of the system.

(c) Show that T1 > Tf > T2.

(d) With the result of part (b), discuss what happens if C1 = 0 or C2 = 0. What about if C1 → ∞ or C2 → ∞? Interpret your results