Two infinitely long parallel rods carrying uniform charge density lambda are at a distance d from each other. Find the electric force on a particle of charge q_* located a distance d directly left of one of the rods. (Derive the formula using Gauss' Law)

**Convert all units to MKS**

1. In some collisions, KE is less after the collision than before. Since energy

cannot be lost, what happened to it? What could you do to show this is true?

2. A 2.00g bullet strikes a 2.00kg block hanging from a long cord. The bullet imbeds itself in the block causing the block with bullet embedded to swing upwards to a height of 50.0 cm above its original position.

A. What type of collision best describes the bullet striking the block?

B. Do a walk-through of the energy of the system starting just before the bullet strikes the block and continue until the block and bullet reach max height.

C. Find the velocity of the bullet before it collides with the block.

3. A 450g rubber ball is dropped from 2.0m above the floor. After the bounce, the ball only rises to a height of 1.5m above the floor.

A. Determine the change in momentum of the ball when it hits the floor and bounces up. (hint: either use motion equations or conservation of energy to determine the speed of the ball when it reaches the floor.)

B. Calculate the amount of heat generated when the ball hits the floor.

C. Explain how momentum is conserved when the ball collides with the floor.

Two capacitors C₁ = 3.2 ?F, C₂ = 13.5 ?F are charged individually to V₁ = 19.0 V, V₂ = 5.6 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.

1.Calculate the final potential difference across the plates of the capacitors once they are connected.

2.Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

3.By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

The energy released in the most energetic hydrogen bombs is often expressed in terms of how much TNT it would take to create the same energy release. The energy content of a large H-bomb is often expressed in megatons (1 megaton = 1 million tons of TNT). In more commonly used units, a megaton corresponds to 4.2 x 1015 Joules of energy, where a Joule is the kinetic energy of a softly hit tennis ball.

Given that information, calculate how much energy was released when the KT impactor hit the Earth 65 million years ago. Express your answer in terms of how many megaton H-bombs it would take to produce the same amount of energy. The energy released corresponds to all of the original kinetic energy of the incoming asteroid, which was moving at an estimated speed of 50 km/sec. Assume that the asteroid was spherical and had a diameter of 12 kilometers and a density of 3000 kg/m3.

Remember that the mass m of a body is its density times it volume. And use the fact that the kinetic energy of a body moving at velocity v is ½mv2. (Youll have the answer in Joules if you use kilograms for mass and meters/sec for the velocity.)

(b) Consider a 1D lattice with a two atom basis with N+1 atoms in total.

a. How many normal modes of vibration are there?

b. Draw a dispersion diagram to illustrate these modes.

c. Describe the motion of the atoms at three key points on the dispersion curve for a longitudinal vibration.

d. How can you interpret the principal quantum number, nk, for the k th vibrational mode?

e. In which branches and regions of the dispersion curve is an electromagnetic wave most likely to interact with the lattice vibration? Explain your answer.

The intensity of reflection of various wavelengths of light projected onto the eye can be used to determine the thickness of the tear film that coats the cornea. The tear film and cornea have indices of refraction 1.331 and 1.373, respectively. When white light is incident on the cornea, strong reflected intensities appear at wavelengths (in air) of 480 nm and 520 nm, but no wavelengths between them. What is the thickness of the tear film?

How much energy Δ? would be required to move the Moon from its present orbit around Earth to a location that is twice as far away? Assume the Moon’s orbit around Earth is nearly circular and has a radius of 3.84×108 m.

Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 4.80 m above the parking lot, and the school building's vertical wall is h = 6.30 m high, forming a 1.50 m high railing around the playground. The ball is launched at an angle of θ = 53.0° above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.) A man on the ground kicking a ball to children on a flat rooftop is shown. The distance between the man and the building is labeled d. The height of the building is labeled h. The motion of the ball is depicted as a parabola originating from the man on the ground and ending at the rooftop. The vector of the initial motion of the ball makes an angle θ with the horizontal. (a) Find the speed (in m/s) at which the ball was launched. 18.12698 Correct: Your answer is correct. m/s (b) Find the vertical distance (in m) by which the ball clears the wall. 1.833 Correct: Your answer is correct. m (c) Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands. 4.06 Correct: Your answer is correct. m (d) What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec2(θ) = 1 + tan2(θ).) 37.45 Incorrect: Your answer is incorrect. What is the final x-position? The final y-position? How much time does it take the ball to travel to the final x-position in terms of the angle? Using this result in the equation for the final y-position, you should be able to write a quadratic equation for tangent of the angle. Be sure to use the trigonometric identity in the hint. ° above the horizontal (e) What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case?

Two cannons are mounted as shown in the drawing and rigged to fire simultaneously. They are used in a circus act in which two clowns serve as human cannonballs. The clowns are fired toward each other and collide at a height of 1.05 m above the muzzles of the cannons. Clown A is launched at θA = 76.0° angle, with a speed v0A = 9.50 m /s. The horizontal separation between the clowns as they leave the cannons is d = 5.55 m. Find the launch speed v0B and the launch angle θB (>45.0°) for clown B. magnitude m/s direction °.

I need an analysis and a complete description of the physics of the mass and magnet falling through the conducting tube demonstration.

1. Describe what a grounding wire does. ( In detail)

2. Is electrostatics a contact or field force? And how do we know that?

Consider a particle with initial velocity v? that has magnitude 12.0 m/s and is directed 60.0 degrees above the negative x axis.

A) What is the x component v? x of v? ? (Answer in m/s)

B) What is the y component v? y of v? ? (Answer in m/s)

C) Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 m.How long tg does it take for the balls to reach the ground? Use 10 m/s2 for the magnitude of the acceleration due to gravity.

To monitor the breathing of a hospital patient, a thin belt is girded around the patient's chest as in the figure below. The belt is a 160 turn coil. When the patient inhales, the area encircled by the coil increases by 40.0 cm2. The magnitude of earth's magnetic field is 50.0

At the Earth's surface, a projectile is launched straight up at a speed of 10.5 km/s. To what height will it rise? Ignore air resistance