A particle with speed V1= 75 m/s makes a glancing elastic collision with another particle that initially is at rest. Both particles have the same mass. After the collision, the struck particles moves off at an angle that is 45 degrees above the line along V1. The second particle moves off at 45 degree below this line. The speed of the struck particle after the colllision is approximately.

A: 38 m/s

B: 82 m/s

C: 64 m/s

D: 47 m/s

E: 53 m/s

Consider a thin spherical shell located between r = 0.49a₀ and 0.51a₀. For the n = 2, l = 1 state of hydrogen, find the probability for the electron to be found in a small volume element that subtends a polar angle of 0.11° and an azimuthal angle of 0.25° if the center of the volume element is located at: θ=5°, ϕ=35°.

1.Consider a negative point charge. Sketch electric field lines, including their direction.

2 Calculate electric field of 1 electron at a distance of 0.1 nanometer away from it. Express your answer in SI units.

3 Consider a point charge of 1 C and calculate its electric field at a distance of 1 m.

Consider a sheet of paper with a thickness of 0.1 mm and a dielectric constant of 3. Suppose we would like to make a 1 F capacitor using this sheet as a spacer between two metallic plates.

Suppose we took out the paper dielectric (while keeping somehow the distance between the plates the same).

1.26: What is the charge after the paper sheet is out completely?

1.27: What is voltage across the capacitor after the paper sheet is out completely?

1.28: How much work does it take to remove the sheet? Explain the sign of your answer.

1.29: How will the answer to 1.28 change is the capacitor remains connected to the 1V battery during the sheet removal.

A small solid sphere of mass M₀, of radius R₀, and of uniform density ρ₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.

The new sphere has mass M = M₀ and density ρ < ρ₀

The new sphere has radius R > R₀ and density ρ = ρ₀
The new sphere has radius R > R₀ and density ρ < ρ₀

The new sphere has density ρ = ρ₀ and mass M < M₀

The new sphere has radius R = R₀ and mass M < M₀

The new sphere has mass M = M₀ and radius R < R₀

Let's figure out the energy and momentum associated with that motion.

For the purposes of this problem, treat the Earth as a solid, uniform sphere with mass 5.97×10²⁴ kg and radius 6.37×10⁶ m , and assume that the Earth's orbit around the sun is circular with a radius of 1.5×10¹¹ m .

Part A

What is the angular kinetic energy of the Earth due to its orbit around the sun?

Part B

What is the magnitude of the Earth's angular momentum due to its orbit around the sun?

Part C

What is Earth's angular kinetic energy due to its rotation around its axis?

Part D

What is the magnitude of the Earth's angular momentum due to its rotation around its axis?

Part E

Remember that energy and momentum are always conserved (though energy can change forms). In other words, if you start with a certain amount of energy and momentum, you must end with the same amount of energy and momentum. By conservation of energy and momentum, the values you've calculated in this problem must have come from somewhere.

Which of the following best explains where the Earth's angular kinetic energy and momentum came from?

Remember that energy and momentum are always conserved (though energy can change forms). In other words, if you start with a certain amount of energy and momentum, you must end with the same amount of energy and momentum. By conservation of energy and momentum, the values you've calculated in this problem must have come from somewhere.

Which of the following best explains where the Earth's angular kinetic energy and momentum came from?

Two identical twins hold on to a rope, one at each end, on a smooth, frictionless ice surface. They skate in a circle about the center of the rope (the center of mass of the two-body system) and perpendicular to the ice. The mass of each twin is 78.0 kg. The rope of negligible mass is 4.0 m long and they move at a speed of 4.90 m/s.

(a) What is the magnitude, in kg · m²/s, of the angular momentum of the system comprised of the two twins?

(b) They now pull on the rope and move closer to each other so that the rope between them is now half as long. Determine the speed, in m/s, with which they move now.

(c) The two twins have to do work in order to move closer to each other. How much work, in joules, did they do? This is the same as the change in kinetic energy.

A 30 kg projectile is launched from the ground at an initial velocity of 300 m/s at an angle of 45 degrees above the horizontal. If air resistance is ignored, determine the following:

a. The projectile's speed at 2000 meters above the ground.

b. The total amount of energy the object has at 3000 m.

c. The maximum height of the projectile.

d. The maximum distance the projectile travels horizontally.

1. Provide an example of an inertial frame of reference and a non-inertial frame of reference. Explain the difference.

2. Using the Michelson-Morley experiment as an example, explain why classical mechanics was unable to explain natural phenomena.

3. Using at least one of Einstein's "thought-experiments", explain how special relativity addresses how it is possible for observers in two different inertial reference frames to “disagree” about time and distance intervals.

4. Describe how special relativity explains the conditions under which classical mechanics breaks down. (When would you, as an observer begin to notice the effects of time dilation and length contraction?)

5. In the early 20th century, the law of conservation of mass was replaced by the law of conservation of mass-energy. Why was this change needed, and how does E=mc² relate to the special theory of relativity?

a) The operator aˆ satisfies the equation [aˆ, aˆ†] = n. Prove that n is a real number. [Hint: Apply the Hermitian conjugation operation “†” to the above equation.]

b) Consider the Hamiltonian Hˆ = h ̄ωˆa†ˆa, where ω > 0 is a real parameter. Prove that Hˆ is Hermitian.

c) Let |ψ〉 be an eigenstate of the above Hamiltonian with the energy ε. Use the commutation relations from part a) to prove that aˆ†|ψ〉 is also an eigenstate of Hˆ. Find the energy of the state aˆ†|ψ〉. You do not need to prove that aˆ†|ψ〉 ≠ 0.

d) Let n > 0. Use the commutation relations to find the ground state energy of Hˆ .

In an apartment building, water is traveling up inside a pipe that has a constant cross-sectional area.

(A.) Which of the following statements about this situation are true? Choose the two correct statements.

As the water rises¸ it slows down

As the water rises¸ its speed stays the same

As the water rises¸ the pressure drops

As the water rises¸ the pressure stays the same

(B.) The flow from a 2 cm diameter shower head pipe is 5 liters per minute. What is the speed of the water exiting the pipe? _______ m/s

(C.) The shower head above is in a fourth floor apartment, 15 meters above the main pipe in the building basement. The main pipe in the basement is 10 cm in diameter. What must the water speed be in the main pipe? ______ m/s

(D.) A fourth floor apartment is 15 meters above the main pipe in the building basement. The flow from a 2 cm diameter shower head pipe is 5 liters per minute. The main pipe in the basement is 10 cm in diameter. What must the pressure (in kPa) in the main pipe in the basement be in order to generate that flow on the fourth floor? Take g to be 9.8 N/kg and atmospheric pressure to be 101.3 kPa.
_______ kPa

(A.) A "healthy" systolic (during heart contraction, the high number in 120/80) blood pressure is typically 120 mmHg. What is this in Pascals? (Take the density of mercury to be 14 g/ml and the acceleration due to gravity to be 10 m/s^2) _____ Pa

I tried converting mmHg to atm (760mmHg = 1atm) and then converting atm to Pa (1 atm = 101325 Pa) and got 15998.6842 Pa, but this answer was incorrect.

(B.) Blood flows through the aorta, and the rest of the body, at a rate of 5 liters per minute.

If the aorta has a diameter of 2 cm, what is the speed of the blood flowing through it? _____ m/s

(C.) Given that the blood flow through the body is 5 liters per minute, estimate the number of capillaries there are in the body using the following. Assume the diameter each capillary is 10 micrometers and the speed of blood through them is 0.03 cm/s

(D.) During a ventricle contraction, the average pressure pushing blood into the aorta is 100 mmHg. What is this pressure in Pascals? (use the density of mercury at 14 g/ml and the acceleration due to gravity of 10 m/s^2)

______ Pa

(E.) During a contraction, the heart pumps 75 ml of blood into the Aorta. Given the pressure above, how much work is done (in Joules) on the blood by the heart during a contraction?

(F.) Assuming a heart rate of 60 beats per minute, how many Calories (kilocalories) are burned just circulating blood during a day. (Take the approximation of 4 Joules per calorie.)

A 62.0-kg boy and his 36.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.10 m/s toward the west. Ignore friction.

(a) Describe the subsequent motion of the girl.

She will move west, in the same direction as her brother, with a speed 3.10 m/s.She will move east, directly away from her brother with a speed 6.89 m/s.    She will move east, directly away from her brother with a speed 5.34 m/s.She will move east, directly away from her brother with a speed 1.55 m/s.

(b) How much potential energy in the girl's body is converted into mechanical energy of the boy–girl system?
J

(c) Is the momentum of the boy–girl system conserved in the pushing-apart process?

YesNo    

(d) If so, explain how that is possible considering there are large forces acting. (If momentum is not conserved, enter "Momentum is not conserved.")

This answer has not been graded yet.

(e) If so, explain how that is possible considering there is no motion beforehand and plenty of motion afterward. (If momentum is not conserved, enter "Momentum is not conserved.")

a) A block of Aluminum has a density of 2700 kg/m^3 and a mass of 63 grams. The block is tied to one end of a string and the other end of the string is tied to a force scale. The block is allowed to hang in the air from the string. Calculate the force which will be registered on the scale.

b) The block remains tied to the string but is now completely submerged in a container of water. The block is not touching the sides or bottom of the container. Calculate the force which will be registered on the scale.

c) The block is raised so that it is only 39% submerged in the water. Calculate the force which will be registered on the scale.