An isolated conducting sphere of radius R has charge Q uniformly distributed on its surface. What is the electric field (E) inside the conducting sphere at distance r = R/2 from center?

Two charges, q₁ = 32 μC and q₂ = 38 μC, are located along a straight line at x = 22 cm and 38 cm respectively. Where along the x-axis should a third charge q₃ with a charge of 1 μC be located such that the net force on this charge is zero.

Two charges, q₁ = 10.5 μC and q₂ = -4.5 μC , are located at coordinates (x,y) = (21.6, 8.6) cm and (23.0, 10.6) cm respectively. Find the electrostatic force between these two changes (take an attractive force to be negative)

Two identical charges of 2.0 μC are located along the y-axis at +5.5 cm and -5.5 cm respectively. Calculate the net electric field strength at a point P located at 17.6 cm along the x-axis.

What force would be experienced by a 6.5 μC charge placed at the point P in the above problem?

The heat is both diffusing and advecting in a 1-d domain [0, 1]. The temperature satisfies the equation ut = Duxx − cux − λu, 0 < x < 1, t > 0, u(0, t) = 1, u(1, t) = 1, t > 0, u(x, 0) = u0(x), 0 ≤ x ≤ 1. (a) Determine whether there exists a steady state. Find the steady state if it exists. (b) When the steady state exists, graph the steady-state temperature distribution in the interval and analyze how heat is flowing in the interval and through its boundaries. You may pick specific values for the graph.

Consider an object that begins rolling from rest at the top of an inclined plane. Assume that there is no slipping between the object and the ramp, and that the bottom of the ramp is defined as h = 0.

1. What form(s) of energy does the object have at the top of the ramp, before it begins moving?

   (a) Gravitational Potential (c) Rotational Kinetic (b) Translational Kinetic (d) Thermal

2. What form(s) of energy does the object have when it has just reached the bottom of the ramp? (a) Gravitational Potential (c) Rotational Kinetic

   (b) Translational Kinetic (d) Thermal

3. Using your answers to #1 & #2, write an equation that describes energy conservation for the object.

4. How is the angular velocity of rotation, ω, related to the center of mass velocity, v, for an object with radius r?

   (a) ω=v·r (b) ω=v·r2 (c) ω=v/r (d) ω=v2/r

5. Using your answers to #3 & #4, solve for the final velocity of the rolling object as a function of its initial height and other physical parameters.

(a) Find the force P that must be applied to a piston of area 12.10 cm² to produce sufficient fluid pressure to support a car weighing 11,851 N by means of a column of fluid of cross sectional area 250 cm² as seen in the figure below.


(b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m.


(c) How far must the smaller piston move in order for the larger one to move 1.00 m?


(d) Calculate the work done by P in moving the smaller piston.


Compare your answer with the answer to part b.

A 1.25 kg block is attached to a spring with spring constant 18 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 42 cm/s What is the amplitude of the subsequent oscillations?

What is the block's speed at the point where x=0.25A?

The atomic mass number of copper is 64. Assume that atoms in solid copper form a cubic crystal lattice. To visualize this, imagine stacking tiny sugar cubes into a big cube. If you pretend there is a copper atom in the middle of each sugar cube, then dissolve the sugar away, the copper forms a cubic lattice. What is the smallest distance between copper atoms?

Hint: The answer is 0.228nm, but you must still show all your work with clear understanding!

Three point-like charges: q₁=9.8 μC, q₂=4.8 μC and q₃=-9.6 μC, are positioned at the corners of an equilateral triangle with side length L= 3.9 cm shown in the figure below.

Find electrostatic forces F₁, F₂ and F₃ exerted on each of the respective charges in terms of their components with respect to shown axes:

F_1x= ___N,  

F_1y= ___N.

F_2x= ___N,

F_2y= ___ N.

F_3x= ___ N,

F_3y= ___ N.

Check if your numerical results (at least approximately) agree with the statement that the total force F=F₁+F₂+F₃ exerted on this whole system must be zero.

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Consider a uranium nucleus to be sphere of radius R=7.4×10−15mR=7.4×10−15m with a charge of 92e distributed uniformly throughout its volume. (a) What is the electric force exerted on an electron when it is 3.0×10−15m3.0×10−15m from the center of the nucleus? (b) What is the acceleration of the electron at this point?

I need a hand written and explained solution

A loaded truck of mass 3000 kg moves on a level road at a constant speed of 6.000 m/s. The frictional force on the truck from the road is 1000 N. Assume that air drag is negligible. (a) How much work is done by the truck engine in 10.00 min? (b) After 10.00 min, the truck enters a hilly region whose inclination is30∘and continues to move with the same speed for another 10.00 min. What is the total work done by the engine during that period against the gravitational force and the frictional force? (c) What is the total work done by the engine in the full 20 min?

1. A 170 g copper bowl contains 110 g of water, both at 23.0°C. A very hot 370 g copper cylinder is dropped into the water, causing the water to boil, with 4.17 g being converted to steam. The final temperature of the system is 100°C. Neglect energy transfers with the environment. (a) How much energy is transferred to the water as heat? (b) How much to the bowl? (c) What is the original temperature of the cylinder? The specific heat of water is 1 cal/g·K, and of copper is 0.0923 cal/g·K. The latent heat of vaporization of water is 539 Cal/kg.

2. One liter of a gas with γ = 1.30 is at 369 K and 1.98 atm pressure. It is suddenly compressed adiabatically to 1/9 its original volume. (a) Find its final pressure and (b) temperature. (c) The gas is now cooled back to 369 K at constant pressure. What is its final volume?

What are the limitations of forward-bias, if any, on a semiconductor diode?

What are the limitations of reverse-bias, if any, on a semiconductor diode?

What portion, if any of the volt-ampere characteristic of the diode (when it is forward-biased) is linear?

What can you say about the d-c resistance of the diode over this linear portion?

3) You are working with a lab instrument that has a diffraction grating of 600lines/mm. 450nm wavelength light passes through the grating and hits a screen 2m away from the grating.

a. What is the spacing between the lines of the grating? b. Given this spacing, what is the distance between two bright spots on the screen? c. If you instead send red (650nm) light through the screen, would this increase or decrease the spacing on the screen? Find the distance between two bright spots with red light.

A bicycle racer sprints at the end of a race to clinch a victory. The racer has an initial velocity of 11.2 m/s and accelerates at the rate of 0.3 m/s2 for 6.9 s.

a)The racer continues at this velocity to the finish line. If he was 293 m from the finish line when he started to accelerate, how much time did he save (in s)?

b)One other racer was 5 m ahead when the winner started to accelerate, but he was unable to accelerate, and traveled at 11.5 m/s until the finish line. How far ahead of him (in seconds) did the winner finish?

c) How far ahead of him (in meters) did the winner finish?

A fast elevator in a skyscraper is employing the following scheme to get from the starting level to the desired level: For the first half of the time it accelerates at the maximum allowed acceleration of 1.0 m/s2 and for the second half it decelerates at the maximum allowed acceleration of −1.0 m/s2. How long does it take (in seconds) to go from ground level to the highest level at 80 m elevation?

A track team is practicing for a 4 × 100 m relay race. The first runner, Linda, is running at a constant speed of 8.6 m/s. The next runner, Jenny, will be starting from rest at the 80 m mark. She has an acceleration of 1.0 m/s2. Ideally the two runners meet at the 100 m mark to hand over the baton. At this point, Jenny is still accelerating.

a) How long does it take Jenny to run from the 80-m mark to the 100-m mark?

b) At what distance behind Jenny should Linda be when Jenny starts running? (Assume for simplicity that there is no distance between the two runners when the switch happens.)

c) What’s Jenny’s speed at the 100m mark?