A car can decelerate at -3.25 m/s2 without skidding when coming to rest on a level road.

What would its deceleration be if the road is inclined at 9.2 ∘ and the car moves uphill? Assume the same static friction coefficient.

Classical Mechanics problem:

See if you can prove the so-called virial theorem. This is a statement that relates the average kinetic energy of a stable system to the potential energy of the system. It applies when the force between two particles of the system has a corresponding potentual energy U of the form U = kr^n, where r is the separation of the particles and n is some real number. So, suppose a mass m moves in a circular orbit about the origin in the field of an attractive central force with potential energy U = kr^n. Show that the kinetic energy T of the particle is T = nU/2.

(Please explain briefly)

A frictionless plane is 10.0 m long and inclined at 28.0°. A sled starts at the bottom with an initial speed of 5.70 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed v_i. Both sleds reach the bottom of the incline at the same moment.

(a) Determine the distance that the first sled traveled up the incline.

______m

b) Determine the initial speed of the second sled.

_______ m/s

Hi,

For an electron in a cylindrical box, how do we find the Hamiltonian operator?

A satellite is placed in an elongated elliptical (not circular) orbit around the Earth. At the point in its orbit where it is closest to the Earth, it is a distance of 1.00 × 10^6 m from the surface (not the center) of the Earth, and is moving at a velocity of 5.14 km/s. At the point in its orbit when it is furthest from the Earth it is a distance of 2.00×10^6 m from the surface of the Earth. (Note that the Earth has a mass of 5.97×1024 kg and a radius of 6.37×106 m. )

(a) How fast is the satellite moving when it is at its furthest point from the Earth?

(b) If, at the closest approach to the Earth, the satellite could be deflected so that it had the same velocity as before, but was now traveling directly away from the Earth, how far from the surface of the Earth would it get before it stopped, and then started to fall back to the Earth?

Some fusion reactors use an induction process in which thermal neutrons collide with deuterium particles that are essentially twice as massive (consisting of one proton and one neutron). Consider a scenario in which a neutron is traveling at 1500 m/s when it collides elastically with a deuterium particle that is initially at rest. Find the magnitude of the neutron's recoil velocity (in m/s).

An air hockey puck of mass 0.42 kg is traveling at 3.5 m/s in a direction 30^o North of East when it encounters another puck of mass 0.36 kg traveling 40^o North of West at 2.8 m/s. The pucks were recently handled by my children so now they are sticky and collide inelastically. Find the magnitude of their velocity (in m/s) after the collision.

The figure shows a cross section across a long cylindrical conductor of radius a = 2.97 cm carrying uniform current 27.5 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 2.10 cm, (c) 2.97 cm (wire's surface), (d)3.84 cm?

What is phase space? And also what is relaxation time? ( Thermodynamics)

Charlie kicks a soccer ball up a small incline. On the way up, ball's acceleration has magnitude
jaj = 0:45 m/s2 and is directed in downhill direction. Charlie kicks the ball at the bottom of the
incline and then immediately start to walk up the incline with constant speed. Charlie performs
twi dierent trials.
a) In the first trial, Charlie kicks the ball with initial speed v0 = 3:4 m/s. Charlie is 2.3-m behind
the ball when the ball is at the highest point. What is the speed vC of Charlie?
b) Charlie performs the second trial. He kicks the ball with unknown speed v00
but walks with the same speed vC as in the first trial. Charlie is now 0.8 m behind the ball when the ball is at the
highest point. What is the initial speed v0 of the ball at the bottom of the hill? (Hint: You need to set-up a quadratic equation for v0).

Explain why equipotential surfaces are always perpendicular to the electric field lines. Do equipotential surfaces ever intersect?

1. What were the "flying disks" that crashed near Roswell, NM? Describe the formerly classified program that there were to be used for. Include the relevant physics.

2. What did you hear about Roswell growing up? Were you told the declassified story or the sci-fi one? Have you visited Roswell?

For a fixed plate separation and voltage, what happens to the stored energy as the plates are brought closer together?

For a fixed charge what happens to the capacitance of a parallel plate capacitor if the distance between the plates is increased?

For a fixed charge, what would happen to the capacitance of a parallel plate capacitor if the area of the plates were increased?

What happens to the capacitance if a conductor is placed between the plates?

What is the capacitance of a cylindrical coaxial capacitor with inner radius a=2cm, outer radius b= 4cm, and length L=10cm?

What happens to the capacitance if a dielectric is inserted between the plates?

A dielectric with dielectric constant 4 is inserted between a parallel plate capacitor filling it completely. If the capacitance before the inserting the dielectric was 100pF what is the new capacitance?

For a fixed separation, what happens to the capacitance of a parallel plate capacitor if the charge is increased?

What is true about capacitance?

What is the energy stored in a 1000nF capacitor if there are 2V applied?

An electron is trapped in a square well of unknown width, L. It starts in unknown energy level, n. When it falls to level n-1 it emits a photon of wavelength λ_photon = 2280 nm. When it falls from n-1 to n-2, it emits a photon of wavelength λ_photon = 3192 nm.

1) What is the energy of the n to n-1 photon in eV?

E_{n to n-1} =

2) What is the energy of the n-1 to n-2 photon in eV?

E_{n-1 to n-2} =

3) What is the initial value of n?

n_initial =

4) What is the width, L, of the well in nm?

L =

5) What is the longest wavelength of light, λ_longest, the well can absorb in nm?

λ_longest=

In a container of negligible mass, 4.20×10⁻² kg of steam at 100°C and atmospheric pressure is added to 0.180 kg of water at 48.0°C.

a) If no heat is lost to the surroundings, what is the final temperature of the system?

b) At the final temperature, how many kilograms are there of steam?

c) How many kilograms are there of liquid water?

Please answer all parts and show all work

Please write your work neatly so I could understand it

3. A very long, straight line of charge runs parallel to a very large, planar sheet of charge. The 2 charge density of the line is -2.0 nC/cm and that of the sheet is +0.50 nC/cm^2 . The distance

between the line and the sheet is 8.0 cm. An electron is released at rest, at a location that is halfway between the line and the sheet. Use conservation of energy to calculate the speed of the

electron when it strikes the sheet. (Hint: calculate the potential difference due to line only and then the potential difference due to the sheet only, and add them up to get the potential difference

you need to determine the speed)

4. You have three capacitors, of 10 nF, 20 nF and 30 nF capacitances, and a voltage source of 11

Volts.

A. Connect the capacitors in series and apply the voltage across the network. Calculate the equivalent capacitance of the network, the charge stored in the network, the energy stored in the

network, and the voltage across each capacitor.

B. Connect the capacitors in parallel and apply the voltage across the network. Calculate the equivalent capacitance of the network, the charge stored in the network, the energy stored in the

network and the charge stored in each capacitor.