Consider a conducting sphere of radius R carrying a net charge Q.

a). Using Gauss’s law in integral form and the equation |E| = σ/ε₀ for conductors, nd the surface charge density on the sphere. Does your answer match what you expect? b). What is the electrostatic self energy of this sphere?
c). Assuming the sphere has a uniform density ρ, what is the gravitational self energy of the sphere? (That is, what amount of gravitational energy is required/released when the sphere is assembled.) d). Assuming Q = 1 C and the sphere is made of ironρ M = 7870 kg/m3, is there a radius R such that the gravitationalself-energy is just enough to overcome the electrostatic self energy? If so, nd R.

Your little dog, Fluffy, is excited to see you and jumps straight up in the air to a height of 0.680 m . What is Fluffy's initial speed as she leaves the ground? You can assume that Fluffy is in "Free Fall" (constant acceleration) during the jump.

Correct

Part B

What is the length of time that Fluffy is in the air?

Calculus dictates that
(∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p

(a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V ]

(b) Calculate (∂U/∂V) T,N for a van der Waals gas
[ for which p = nRT/(V–nb) – a (n/V)2 ]

(c) Give a physical explanation for the difference between the two.

(Note: Since the mole number n is just the particle number N divided by Avogadro’s number, holding one constant is equivalent to holding the other constant.)

A basketball player grabbing a rebound jumps 78 cm vertically. How much total time (ascent and descent) does the player spend (a) in the top 12 cm of this jump and (b) in the bottom 12 cm? Do your results explain why such players seem to hang in the air at the top of a jump?

An unknown positive point charge is placed at x = -0.27 m, y = 0 m, a charge of -2.8 micro-coulombs is placed at x = 0 m, y = -0.20 m, a charge of +2.2 micro-coulombs is placed at x = +0.50 m, y = -0.29 m, and charge of +2.8 micro-coulombs is placed at x = 0 m, y = +0.20 m. If the total electric field due to all four charges at the origin is 4.5 x 106 N/C (the x component of the total electric field is positive), what is value of the magnitude of the unknown charge in micro-coulombs? If negative, include a negative sign.

Point charges of 6.75 µC and

−4.00 µC

are placed 0.300 m apart. (Assume the negative charge is located to the right of the positive charge. Include the sign of the value in your answers.)

(a) Where can a third charge be placed so that the net force on it is zero?
m to the right of the

−4.00 µC

charge

(b) What if both charges are positive?
m to the right of the  4.00 µC charge

1. What is light? 2. What are the three models of light? 3. When is each model of light applicable? 4. What is visible light? 5. What is white light? 2-3 sentences each.

A person measures her heart rate by counting the number of beats in 30 s. If 42 ± 1 beats are counted in 30.0 ± 0.5 s, what is the heart rate and its uncertainty in beats per minute?

A 2100-m-high mountain is located on the equator.

How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth's radius is 6400 km.

Express your answer to two significant figures and include the appropriate units.

When the police want to know how fast your car is going, they shoot a "radar gun" at the car. The radar gun emits waves at approximately 24.15 GHz. Those waves reflect off of your car and are detected by the same "radar gun" that emitted them. The detector can detect both frequency and intensity. Using concepts of general physics, explain how the radar gun works. You probably want to draw pictures, use an equation or two, and use words.

In uniform circular motion, which of the following quantities are constant?

Which of these quantities are zero throughout the motion?

a parallel-plate capacitor is oriented horizontally and charged so that there is an electric field of 50,000 V/m pointing up inside the gap of 1cm, which is filled with air. a.) With the charge on each plate remaining constant, the capacitor is immersed half-way in an oil of dielectric constant K=2.5 What is now the potential difference between the plates? b.) If on top of the oil, water (K=80) is poured to completely fill the upper part of the gap, what is now the potential difference between the plates? (since this measurement takes place over a short period of time, please treat water as an insulator, not as a conductor.)

Please do step by step clear and show eqations used. Thank you

A rocket designed to place satellites into orbit is carried to a cruising altitude. When the plane is flying in a straight line and at a constant speed of 850 km/h, the rocket is dropped. After the drop the plane continues to fly at the same pseed and in a straight line. The rocket falls for a bried time, and then its propulsion starts. Once the propulsion starts the combined effects of gravity and thrust give the rocket a non-constant acceleration of (29.43 + 0.44t) m/s^2 directed at an angle of 30.0 degrees above the horizontal. For safety the rocket should be at least 1.00km in front of the plane when it climbs through the plane's altitude. Ignore drag.

a) If the rocket falls for 5.15 s before engaging propulsion, how much total time will pass before the rocket passes back through the cruising altitude of the plane?
b) will the rocket safely pass 1.oo km in front of the plane for this free-fall time of 5.15s? What will be the horizontal distance between the rocket and the plane when they are at the same altitude ?

13.18 Two piano strings with the same mass and the same length are to be tuned to 440 Hz (A on the equal temperament scale). One string, with a tension of 300 N is already tuned to 440 Hz. The second string frequency is 435 Hz. a) Should the tension of string 2 be increased or decreased to tune the frequency to 440 Hz? b) How much must the tension of string 2 be changed to change the frequency from 435 Hz to 440 Hz?

14.2 The wavelength of a 450 Hz sound wave in air has a wavelength of 0.78 m. a) What is the speed of sound in air? b) What is the temperature?