. (a) Draw the basic setup for quantum key distribution.

(b) Explain the “intercept-resend” attack that Eve can attempt (draw a simple figure).

(c) Explain how this attack is thwarted by the quantum key distribution protocol. How can Eve’s attack be detected?

(d) What does the security of quantum key distribution rely on fundamentally?

(part 1 of 2)

An electric car is designed to run on a bank of batteries with a total potential difference of 29 V and a total energy storage of 2.2×107 J. If the electric motor draws 6.8 kW, what is the current delivered to the motor? Answer in units of A.

(part 2 of 2) If the electric motor draws 6.8 kW as the car moves at a steady speed of 47.0 m/s, how far will the car travel before it is “out of juice”? Answer in units of m.

You have set up an experiment where two Stern-Gerlach analyzers sequentially measure spin along the z-axis. The first analyzer allows particles with spin up along z to pass. The second analyzer allows particles with spin down along z to pass. Between the two analyzers is a magnetic field aligned along +x. Your experiment sends identical spin-1/2 particles at speed v along the y-axis through the analyzers, which are separated by a distance Δy. What is the smallest distance Δy that will transmit 50% of the particles passed through the first analyzer through the second analyzer?

Show that if qd≫1 the probability for tunneling through a potential barrier of width d is proportional to e^(-2qd). Plot this function and explain the implications.

While vacationing in the mountains you do some hiking. In the morning, your displacement is S⃗ morning= (2200 m , east) + (4000 m north) + (200 m , vertical). After lunch, your displacement is S⃗ afternoon= (1600 m , west) + (2900 m , north) - (300 m , vertical).

Part A

At the end of the hike, how much higher or lower are you compared to your starting point?

Express your answer with the appropriate units

Part B

What is the magnitude of your net displacement for the day?

Express your answer with the appropriate units.

7. The University Skydiving Club has asked you to plan a stunt for an air show. In this stunt, two skydivers will step out of opposite sides of a stationary hotair balloon 1500 meters above the ground. The second skydiver will leave the balloon 20 seconds after the first skydiver but you want them both to land on the ground at the same time. The show is planned for a day with no wind so assume that all motion isvertical. To get a rough idea of the situation, assume that a skydiver will fall with a constant acceleration of 9.80 m/s2before the parachute opens. As soon as the parachute is opened, the skydiver falls with a constant velocity of 3.2 m/s. If the first skydiver waits 3 seconds after stepping out of the balloon before opening her parachute, how long must the second skydiver wait after leaving the balloon before opening his parachute?

A 65kg skater travelling northward at 3.8m/s accidentally collides with a 75kg skater travelling west at 2.4m/s. They hold on to each other while attempting to regain balance and continue moving in that direction after the collision. What total speed and direction (find angle) do the skaters move together after the collision?

The drive propeller of a ship starts from rest and accelerates at 2.99 x 10-3 rad/s2 for 2.86 x 103 s. For the next 1.90 x 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.61 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.31 rad/s. Find the total angular displacement of the propeller.

Electric Field at a Point

A -70nC charge is distributed uniformly along the x-axis from x = -0.8m to x = 2.6m. Consider a point at y = 1.5m on the y-axis.

a) What is the x-component of the electric field at the point?

b) What is the y-component of the electric field at the point?

c) What is the total magnitude of the electric field at the point?

Thank you

(1)Sphere A is attached to the ceiling of an elevator by a string. A second sphere is attached to the first one by a second string. Both strings are of negligible mass. Here m₁ = m₂ = m = 3.57 kg.

(a) The elevator starts from rest and accelerates downward witha= 1.35 m/s². What are the tensions in the two strings in newtons?

(b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings in newtons?

(c)The maximum tension the two strings can withstand is 92.2 N. What maximum upward acceleration (in m/s²) can the elevator have without having one of the strings break?

(2) Consider the 65.0-kg ice skater being pushed by two others shown in the figure below.

(a)Find the direction (in degrees counterclockwise from the +x-axis) and magnitude (in N) ofF_totthe total force exerted on her by the others, given that the magnitudes F₁ and F₂ are 22.0 N and 15.8 N, respectively. (AssumeF₁points in the positive x direction.)

(b) What is her initial acceleration (in m/s²) if she is initially stationary and wearing steel-bladed skates that point in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(c) What is her acceleration (in m/s²) assuming she is already moving in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(3)Here, m_A = 2.50 kg and m_B = 6.50 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration.

(a) What is the magnitude of the acceleration (in m/s²) of each of the objects?

(b) What is the magnitude (in N) of the tension in the string?

(c)Through what distance (in m) will the two objects move in the first three seconds of motion?

Two thin slits separated by 0.0880 mm are illuminated by light from a He-Ne laser (? = 633 nm), producing interference fringes on a distant screen. Find the angle between the centers of the central bright fringe and the next bright fringe.

How wide would the slits in Young’s two-slit experiment have to become in order for us to end
up in the double slit diffraction situation? Clearly explain your rationale in a maximum of
three succinct sentences.