A Gaussian surface in the form of a hemisphere of radius R = 9.86 cm lies in a uniform electric field of magnitude E = 7.16 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface. What is the flux through (a) the base and (b) the curved portion of the surface?

A 12.0-kg block is pushed across a rough horizontal surface by a force that is angled 30.0◦ below the horizontal. The magnitude of the force is 75.0 N and the acceleration of the block as it is pushed is 3.20 m/s2 . What is the magnitude of the contact force exerted on the block by the surface?

One possibility for a low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1100 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel �spinup.� (a) Make reasonable assumptions (average frictional retarding force = 450 N, twenty acceleration period from rest to 95 km/h, equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and estimate what total energy needs to be stored in the flywheel. (b) What is the angular velocity of the flywheel when it has full �energy charge�? (c) About how long would it take a 150 hp motor to give the flywheel a full energy charge before a trip?

A projectile of mass m = 5kg is thrown upward vertically with a velocity v₀ = 9 m/s

a) Starting with Newton's 2nd Law F_Net = ma, calculate the time to an accuracy of four decimal places at which the maximum height is reached when no air resistance is present.

b) Starting with Newton's 2nd Law F_Net = ma, calculate the time to an accuracy of four decimal places at which the maximum height is reached when considering the following force of air resistance:

F_air = 7.775 x 10^-5v

c) Starting with Newton's 2nd Law F_Net = ma, calculate the time to an accuracy of four decimal places at which the maximum height is reached when considering the following force of air resistance:

F_air = 0.055v²

A 78.0 kg hoop rolls along a horizontal floor so that its center of mass has a speed of 0.190 m/s. How much work must be done on the hoop to stop it?

When a DC current passes through the coil, it will produce a magnetic flux around the coil. Is this the reason why the coil get heated? Because the magnetic flux will be stable after all as DC current does not oscillate?

The deuteron is a bound state of a proton and a neutron of total angular momentum j = 1. It is known to be principally an S(ℓ = 0) state with a small admixture of a D(ℓ = 2) state. Calculate the magnetic moment of the pure d state n-p system with j = 1. Assume that the n and p spins are to be coupled to make the total spin s which is then coupled to the orbital angular momentum ℓ to give the total angular momentum j. Express your result in nuclear magnetons. The proton and neutron magnetic moments are 2.79 and -1.91 nuclear magnetons, respectively.
Note: The nuclear magneton is given by
µ = [(gℓℓ + gss) · j] j(j + 1) jµ0

2 questions thx

1) A point source emits sound waves isotropically. A sound meter measures a sound level of 51.72 dB at location C and a sound level of 45.53 at location D, a distance of 16 m from location C. The two locations C and D and the point source are all located along the same line. How far from location C is the point source? Give your answer in m, though enter only the numerical part in the box.

2) A point source emits sound waves isotropically. A sound meter measures a sound level of 51.21 dB at location C and a sound level of 47.79 at location D, a distance of 15 m from location C. The two locations C and D and the point source are all located along the same line. What is the total output power emitted by the point source? Give your answer in mW, though enter only the numerical part in the box.

A.) What is a power law? What does it mean for a quantity like the electric field to drop off as a power law?

B.) Does the electric field always drop off as r^-2, or can it drop off faster?

C.) Can the Coulomb force do work on a mass? What is required for this to happen?

A helium-filled toy balloon has a gauge pressure of 0.350 atm and a volume of 8.0 liters. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?__________J

Please show all work to get credit.

A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 7.00 m to the right of the slide. The image is 73.5times the size of the slide.

(a) How far is the slide from the lens?
________ m

(b) Is the image erect or inverted?

erectinverted    

(c) What is the focal length of the lens?
_______ m

(d) Is the lens converging or diverging?

convergingdiverging   

7) While pushing a cart across a floor, Andrea and Jennifer exert forces ?? and ?? on the cart. Andrea’s

force is due north with a magnitude of 130.0 N and Jennifer’s force is 32° west of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer’s housemate, David, disagrees with the move and wants to prevent its relocation, with what force should he push with so the cart does not move? (assume there is not friction on the cart)

8) A car with a mass of 1000.0 kg accelerates from 0 to 90.0 km/h in 10.0 s. (a) What is its acceleration? (b) What is the net force on the car?

9) A body of mass ? moves in a horizontal direction such that at time t its position is given by
?(?) = ? cos(?? + ?) where ?, ?, and ?are constants. What is the time dependent force acting on the body

Calculate the curls of: ? ×V~ = [?yVz ??zVy] xˆ +[ ?zVx ??xVz] yˆ+ [?xVy ??yVx] zˆ  

(b) V= y xˆ + z yˆ + x^2 zˆ

The magnitudes of F1, F2 and F3 are 300, 190 and 250 N, respectively. F1 is directed on the slope m =
0.6 m/m. F2 is directed alpha = 0.17 radians from F1. F3 is directed beta =123 degrees from F2.
Determine the direction of the Resultant in degrees measured counter-clockwise from the + x-axis.

A car initially traveling at 40 m/s runs out of gas while traveling up a slope. It coasts for a distance of 500 m before it starts to roll back down.

a. What is the acceleration of the car?

b. What is the angle (incline) of the slope?

c. How long does it take after the car runs out of gas before it starts to roll back down?

d. Once the car starts rolling backwards, how long does it take before it passes its starting point, 500m down the slope?