You have two conducting plates with nothing in between them. Using a voltmeter, you measure the voltage difference between the plates to be 465 V. You release an alpha particle with mass of 6.5×10-27 kg and a charge of 3.2×10-19 C from near the positive plate. What is the kinetic energy of the alpha particle when it reaches the other plate? The distance between the plates is 44.0 cm. b.) You observe an electron move through a uniform electric field. The electron/field-system loses 2480 pJ of electrostatic potential energy as the electron picks up speed. What was the voltage difference between the two points

A disk-shaped parallel plate capacitor is made with a radius of 2 cm and a plate separation distance of 2/π millimeters. The dielectric is in two layers, each of thickness 1/π mm. The first layer is all composed of a material with dielectric constant 9. The second layer is actually made of two materials in a bullseye pattern. The inner circle has radius 1 cm and dielectric constant 6. The annular ring around it has dielectric constant 4. The entire capacitor is charged up on a 360 V and then disconnected from the voltage source. While it is still charged, the plates are moved farther apart to accommodate another layer 1/π mm thick of material with dielectric constant 1. Find the final voltage and charge on the capacitor. Use 9x10^-12 C²/J·m for the permittivity of empty space.

Falling Bodies. In the simplest model of the motion of a falling body, the velocity increases in proportion to the increase in the time that the body has been falling. If the velocity is given in feet per second, measurements show the constant of proportionality is approximately

32. a) A ball is falling at a velocity of 40 feet/sec after 1 second. How fast is it falling after 3 seconds?

b) Express the change in the ball’s velocity ∆v as a linear function of the change in time ∆t.

c) Express v as a linear function of t. The model can be expanded to keep track of the distance that the body has fallen. If the distance d is measured in feet, the units of d ′ are feet per second; in fact, d ′ = v. So the model describing the motion of the body is given by the rate equations d ′ = v feet per second; v ′ = 32 feet per second per second.

d) At what rate is the distance increasing after 1 second? After 2 seconds? After 3 seconds?

e) Is d a linear function of t? Explain your answer.

A particle slides back and forth on a frictionless track whose height as a function of horizontal position x is given by y=ax2, where a = 0.81 m−1 .If the particle's maximum speed is 8.4 m/s , find the turning points of its motion. (x1,x2) in m

Determine the escape speed from (a) Jupiter's moon Callisto, with mass 1.07×1023kg and radius 2.40 Mm, and (b) a neutron star, with the Sun's mass crammed into a sphere of radius 5.60 km .

The magnetic field 41.0 cm away from a long, straight wire carrying current 4.00 A is 1950 nT.

(a) At what distance is it 195 nT?


(b) At one instant, the two conductors in a long household extension cord carry equal 4.00-A currents in opposite directions. The two wires are 3.00 mm apart. Find the magnetic field 41.0 cm away from the middle of the straight cord, in the plane of the two wires.

How far is the point of interest from each wire? nT

(c) At what distance is it one-tenth as large?
cm

(d) The center wire in a coaxial cable carries current 4.00 A in one direction, and the sheath around it carries current 4.00 A in the opposite direction. What magnetic field does the cable create at points outside the cables?
nT

Two in-phase loudspeakers, which emit sound in all directions, are sitting side by side. One of them is moved sideways by 3.0 m, then forward by 7.0 m. Afterward, constructive interference is observed 14, 12, and 34 the distance between the speakers along the line that joins them, and at no other positions along this line.

What is the maximum possible wavelength of the sound waves?

Express your answer with the appropriate units.

To see how two traveling waves of the same frequency create a standing wave.

Consider a traveling wave described by the formula

y1(x,t)=Asin(kx−ωt).

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

a)

Part A

Part complete

Which one of the following statements about the wave described in the problem introduction is correct?

b)

Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves y1(x,t)+y2(x,t), where y1(x,t) is the wave described in Part A and y2(x,t) is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

ys(x,t)=ye(x)yt(t).

This form is significant because ye(x), called the envelope, depends only on position, and yt(t) depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of ye(x).

Part C

Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.

Express your answers in terms of A, k, x, ω (Greek letter omega), and t. Separate the two functions with a comma.

d)

At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?

Express your answer in terms of parameters given in the problem introduction.

Part F

At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.

Express t1 in terms of ω, k, and necessary constants.

The man fires an 80 g arrow so that it is moving at 80 m/s when it hits and embeds in a 8.0 kg block resting on ice.

How far will the block slide on the ice before stopping? A 7.1 N friction force opposes its motion.

An electron experiences the greatest force as it travels 3.0×10⁶ m/s in a magnetic field when it is moving northward. The force is vertically upward and of magnitude 8.0×10⁻¹³ N .

What is the magnitude and direction of the magnetic field?

Part B

The position of a 0.30-kg object attached to a spring is described by

x = (0.22 m) cos(0.3?t)

(a) Find the amplitude of the motion.
m

(b) Find the spring constant.
N/m

(c) Find the position of the object at t = 0.26 s.
m

(d) Find the object's speed at t = 0.26 s.
m/s

A blue car with mass m_c = 497 kg is moving east with a speed of v_c = 16 m/s and collides with a purple truck with mass m_t = 1336 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of θ = 51° South of East

1)

What is the magnitude of the initial momentum of the car?

kg-m/s

2)

What is the magnitude of the initial momentum of the truck?

kg-m/s

3)

What is the speed of the truck before the collision?

m/s

4)

What is the magnitude of the momentum of the car-truck combination immediately after the collision?

kg-m/s

5)

What is the speed of the car-truck combination immediately after the collision?

m/s

6)

Compare the magnitude of the TOTAL momentum of the system before and after the collision:

A man stands on the roof of a building of height 13.4 m and throws a rock with a velocity of magnitude 27.5 m/s at an angle of 32.8 ∘ above the horizontal. You can ignore air resistance.

1. Calculate the maximum height above the roof reached by the rock.

2. Calculate the magnitude of the velocity of the rock just before it strikes the ground.

3. Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

1) Imagine an object moving horizontally with uniform (that is, constant) velocity. Sketch the position time and velocity-time graphs for this motion.

2) Imagine tossing an object straight up into the air, then catching it. Sketch the position-time and velocity-time graphs for this motion, from the moment it leaves your hand to the moment just before it lands in your hand.

3) Imagine tossing a ball slightly upwards and towards another person. Consider the motion from the moment the ball leaves your hand to the moment just before it lands in the other person’s hands. Draw the trajectory for the ball. In how many dimensions is the object moving?

Steam at 100°C is added to ice at 0°C.

(a) Find the amount of ice melted and the final temperature when the mass of steam is 13 g and the mass of ice is 48 g.

(b) Repeat with steam of mass 2.1 g and ice of mass 48 g.

1)Discuss how energy conservation applies to a swinging pendulum. (PLEASE EXPLAIN YOUR ANSWERS, WITHOUT ANY EXPLANATION YOU WILL NOT RECEIVE FULL CREDIT) Where is the potential energy the greatest? The least? Where is the kinetic energy the most? The least? Where is the pendulum moving the fastest? The slowest?

2)Why does the force of gravity do no work on a bowling ball rolling along a bowling alley?