In a shooting field where noone can get hurt, there is a vertical square plastic board, 0.100 m on a side and with mass 0.800 kg , that rotates on a horizontal axis along its top edge. The center of the plastic board is hit by a bullet with mass 1.50 g that is moving with 300 m/s and that stays embedded in the plastic board.

a)Find the angular velocity of the plastic board right after the bullet's hit?

b)Calculate the maximum height above the equilibrium position does the center of the plastic board reach before starting to go back down again?

c)Find the minimum bullet velocity which would be required for the plastic board to swing all the way over after impact?

Assume that a certain billionaire innovator misplaced his supercar and finds it launched into a high-earth orbit at a height of 15 000 km above the Earth’s surface. Wondering if he left his headlights on, he uses his telescope to directly observe the car as it passes overhead.

a. What fundamental physical effect limits the resolution of optical systems? Explain how this physical effect leads to the observed limitation.
b. What fundamental requirement can we set on the telescope to be able to distinguish the two front lights of the supercar if they are separated by 1.5m and emit light at a wavelength of 575 nm?

1. Imagine that you’re sledding alone down a steep hill on a toboggan and that you left the top of the hill at the same time as an identical toboggan, loaded with 4 people.

a. Which toboggan will reach the bottom of the hill first?

b. If you took a toboggan down a 2% grade slope, for a 1000 foot run, and then you took the toboggan down a steeper route of 15% grade down the hill, how would that affect the speed of your descent? Explain.

c. Before each downhill run, you must pull the toboggan back to the top of the hill. If the Hill is 1000 vertical feet, how many runs will you do in 2 hours?

d. Why can you sled down a hill? But you can’t you skate down a hill?

e. How do snow shoes help you walk in snow? Why are their different sized snow shoes?

2. a. Why is hip movement and turning the knees important in improving a golf swing?

b. During the back swing, are you accelerating?

c. At the moment you reach the bottom of the swing you make contact with the ball. Explain how energy is transferred from the club to the ball

d. Why is there more stress on a golfers shoulders at the start of the swing, than when hitting the ball?

e. Why do you need to follow through on the swing?

f. What has happened when a golf shot is hooked?

g. What is the sweet spot on a club and what does it do?

h. What is a ping sound and how is it produced when hitting a golf ball?

A small block with mass 0.0400 kg slides in a vertical circle of radius 0.500 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 4N . In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.660 N .
How much work was done on the block by friction during the motion of the block from point A to point B?

5 kg of saturated water mixture in a rigid container initially at the standard pressure (state 1) is heated at constant volumeto a pressure of 35 MPa (state 2). This heating is performed in such a way that the process passes through the critical point of the water:

a) What is the volume in m3 occupied by the vapor phase and the liquid phase of the mixture at the initial condition (state 1)?
b) Determine the change in internal energy between the initial state and final state of the process.

The standard pressure is 101.325 kPa.

Gaseous calcium atoms absorb light at 423, 272, and 240 nm. After a photon of 272 nm is absorbed from the ground state, a photon of wavelength 672 nm is emitted. After absorption of a photon of 240 nm occurs from the ground state, a photon is emitted of wavelength 504 nm.

1. After the 504 nm photoemission occurs, what wavelength of light (in nm) would have to be emitted for an electron to return to the ground state? Construct an energy diagram to help.

2. What is the energy difference between the second highest and third highest states? Construct an energy diagram to help.

Is your electric blanket safe? It has been theorized that excess nighttime exposure to electromagnetic fields may reduce the production of the hormone melatonin in certain women. Furthermore, reduced melatonin levels might lead to an increased risk of breast cancer. Scott Davis at Seattle's University of Washington School of Public Health and Community Medicine was one of the first to investigate links between electromagnetic fields and cancer (particularly leukemia). He has been quoted as saying, "Electric blankets were pretty effectively re-engineered a number of years ago. Modern-day electric blankets ? anything you buy in the store now ? (has a different) configuration of the heating elements in the blanket so that it doesn't produce any magnetic fields." How could the wiring in an electric blanket be designed to minimize or eliminate the production of external magnetic fields?

A long, uniform rod of length  0.500 mm and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.42 rad/srad/s and a moment of inertia about the axis of 3.20×10⁻³ kg⋅m2kg⋅m2 . An insect initially standing on the rod at the axis of rotation decides to walk to the other end of the rod. When the insect has reached the end of the rod and sits there, its tangential speed is 0.173 m/sm/s . The insect can be treated as a point mass.

A) Find the mass of the rod?

B)  Find the mass of the insect?

A square plastic chunk with mass 0.750 kg is suspended from the lower end of a light cord that is 1.66 mm long. The plastic chunk is stay still in the beginning without any motion. A bullet with mass 0.0132 kg is on the way to the plastic chunk with a horizontal velocity v0. The bullet hits the plastic chunk and then embedded in it. After collision, combined bullet and plastic chunk swings on the end of the cord. When the plastic chunk has risen a vertical height of 0.800 mm , the tension in the cord is 4.98 N .
What was the initial velocity v0 of the bullet?

Consider a harmonic electromagnetic plane wave with angular frequency ω and propagation vector k=(kx,ky,kz) (i.e., propagating in an arbitrary direction). The electric field vector is E=(Ex,Ey,Ez) with amplitudes (Exo,Eyo,Ezo) and the magnetic field vector is B=(Bx,By,Bz) with amplitudes (Bxo,Byo,Bzo).
a) Write an expression for the electric and magnetic waves using complex representation.
b) Using the laws of electromagnetism without sources (Maxwell’s equations in free space), prove that k × E = ωB, and k · E = 0
c) What does part b) tell you about the relative directions of k, E and B?

32.) In the plane of a square conducting frame with the sides a= 8cm, there is an infinite long wire in a distance b= 0.5cm parallel with one side of the square. The infinite wire carries a current with the time functionI(t) = I₀·cos(ωt), where I₀= 3A,ω= 2pi·f and the frequency is f= 3MHz.

a./ Find the mutual induction coefficient between the wire and the square.

b./ Find the amplitude of the induced voltage.c./ Find the maximal magnetic flux in the square.

A football receiver running straight downfield at 5.50 m/s is 10.0 m in front of the
quarterback when a pass is thrown downfield at 25.0 degree above the horizon. If the
receiver never changes speed and the ball is caught at the same height from which it
was thrown:

(a) Draw a diagram of the motion. Include initial and final positions of the runner.

(b) Find the initial speed of the football.

(c) Find the amount of time the football spends in the air

(d) The distance between the quarterback and the receiver when the catch is made.

a rocket rises vertically from rest, with an acceleration of 3.2 m/s(s) until it runs out of fuel at an altitude of 845 m. After this point, its acceleration is that of gravity, downward. what is the velocity when the rocket runs out of fuel? how long does it take to reach that point? what is the maximum altitude and how long to reach it? what is the velocity when it strikes earth? how long is the rocket in the air?

A uniform magnetic field B is directed into the page. A circular circuit of radius r containing a
resistor R and a capacitor C, is placed in this field. Initially the capacitor is uncharged, and at time t =
0, the magnitude of the magnetic field starts to change at a rate dB/dt = x, x > 0.
a) Using Lenz’s law, determine the direction of the induced current in the closed loop. Justify
your answer.
b) Calculate the induced emf Ɛ and draw its direction.
c) Write an equation for the circuit as a function of time.
d) Q(t) for this circuit is given as Q(t) = C Ɛ (1−e −t/RC); what is the voltage VC across the
capacitor as a function of time?
e) What is the power dissipated by the resistor at t = 0 ?

A mass spectrometer is designed to calculate masses of atoms. A source produces positive ions of
mass m and charge q. The ions move with a velocity v to the right, pass through a narrow slit S1 and
enter a region between two charged plates. In this region they experience both an electric and a
magnetic field. The electric field E is caused by the 2 charged plates; the upper plate is (-) charged
and the lower plate is (+) charged. The magnetic field is B1 and points out of the page. The ions
exit this region through slit S2 . When they exit, they experience a new magnetic field B2, that is also
directed out of the page. The ions are then collected inside a collector.
a) Draw the electric field between the charged plates.
b) With what velocity should ions enter in order to follow a straight trajectory from S1 to S2?
c) Draw the trajectory followed by the ions in the region of magnetic field B2? Why does the
trajectory look like this?
d) Where should the collector be placed in the plane containing S2 to collect the ions?
e) What is the mass of the ion in terms of field strengths, charge, and S2-collector distance?