1. A roller coaster car has a mass of 250 Kg. The car is towed to the top of a 30 m hill where it is released from rest and allowed to roll.   The car plunges down the hill, then up an 8 m hill and through a loop with a radius of 8 m. Assuming no friction: (8 points)

1. What is the potential energy of the car at the top of the 30 m hill?

2. What are the Kinetic Energy and the speed of the car at the bottom of the 30 m hill?

3. What are the Kinetic Energy and the speed of the car at the top of the 8 m hill?

4. If the hill makes an angle of 60 ° with the horizontal and the car takes 15 seconds to be towed up the 30 m hill, determine the length of the hill, the velocity of the car, the force required to tow the car up the hill, and the power of the motor pulling the car up the hill.

Please type your answer, Please do not write on the Paper and Post t.

A particle of mass 0.350 kg is attached to the 100-cm mark of a meterstick of mass 0.150 kg. The meterstick rotates on the surface of a frictionless, horizontal table with an angular speed of 6.00 rad/s.

(a) Calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 50.0-cm mark.

(b) Calculate the angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 0-cm mark.

Two long straight parallel wires are 11 cm apart. Wire A carries 2.0-A current. Wire B's current is 5.0 A in the same direction.

Determine the magnetic field magnitude due to wire A at the position of wire B.

Determine the magnetic field due to wire B at the position of wire A

Are these two magnetic fields equal and opposite?

Determine the force per unit length on wire A due to wire B.

Determine the force per unit length on wire B due to wire A.

Are these two forces per unit length equal and opposite?

3) The very first magnetic resonance imaging (MRI) devices employed multi-layer copper solenoids, like the one shown in the figure below. The solenoid dimensions were: length = 2 m and inner radius = 0.4 m. The required magnetic field was 0.3 T. Due to thermal considerations, the copper wire conductor was chosen to have a square cross-section, 10 mm×10 mm, which limited the maximum current in the conductor to 1,000 A.

A) What is the minimum number of solenoid layers needed to achieve the required magnetic field? Assume that the conductor in each layer is tightly wound on a cylinder, without any gaps.

B) For the chosen number of layers and using the copper resistivity value at room temperature, estimate the electrical power consumption of this solenoid at 0.3 T.

This year, three scientists won the Nobel Prize in Physics. Give a brief summary of their research and provide examples of common applications of their work.

A sinusoidal wave is traveling on a string with speed 34.9 cm/s. The displacement of the particles of the string at x = 5.9 cm is found to vary with time according to the equation
y = (3.9 cm) sin[1.2 - (7.1 s^-1)t].
The linear density of the string is 4.8 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t) = y_m sin(kx - ωt),
what are (c) y_m, (d) k, and (e) ω, and (f) the correct choice of sign in front of ω? (g) What is the tension in the string?

Consider a beam of white light striking a face of an equilateral prism at an incident angle of Theta(1)= 50

IP A charge of 18.0 μCμC is held fixed at the origin.

Part A:

If a -7.00 μCμC charge with a mass of 3.40 gg is released from rest at the position (0.925 mm, 1.17 mm), what is its speed when it is halfway to the origin?

Part B:

Suppose the -7.00 μCμC charge is released from rest at the point xx = 1212(0.925mm) and yy = 1212(1.17mm). When it is halfway to the origin, is its speed greater than, less than, or equal to the speed found in part A?

Suppose the -7.00  charge is released from rest at the point  = (0.925) and  = (1.17). When it is halfway to the origin, is its speed greater than, less than, or equal to the speed found in part A?

Part D

Find the speed of the charge for the situation described in part B.

In a Young's double-slit experiment, two parallel slits with a slit separation of 0.135 mm are illuminated by light of wavelength 579 nm, and the interference pattern is observed on a screen located 4.15 m from the slits.

(a) What is the difference in path lengths from each of the slits to the location of the center of a fifth-order bright fringe on the screen?
µm

(b) What is the difference in path lengths from the two slits to the location of the center of the fifth dark fringe away from the center of the pattern?
µm

a)An infinite (very large) charged plate with charge density σ is parallel to the xz plane and passes through the point (0, 5, 0). Calculate the electric field of the plate.
For points and> 5, where is the electric field directed? How much is E⃗
for points and <5 where is the electric field directed? how much is E⃗
b) Thinking about the previous example, now in addition to the loaded plate from the previous exercise, think that there is an extra plate with −σ load density, parallel to the xz plane but passing through the origin.
Calculate the electric field E⃗ for points between the plates.
(This system is called a condenser.)

A concave mirror has a focal length of 63.6 cm.

(a) What is its radius of curvature?

__________ cm

(b) Locate the image when the object distance is 100 cm. (Indicate the side of the mirror with the sign of your answer.)
____________ cm

Describe the properties of the image when the object distance is 100 cm. (Select all that apply.)

A) real

B) virtual

C) upright

D) inverted

(c) Locate the image when the object distance is 10.0 cm. (Indicate the side of the mirror with the sign of your answer.)
________ cm

Describe the properties of the image when the object distance is 10.0 cm. (Select all that apply.)

A) real

B) virtual

C) upright

D) inverted

Kinetic friction is a constant-value force, while static friction changed in response to other forces, up to some maximum.  Why is this the case? What if static friction behaved more like kinetic friction, with same constant value?

How far would you have to drill into the Earth, to reach a point where your weight is reduced by 7.5% ? Approximate the Earth as a uniform sphere.

An astronaut wants to determine the mass of objects she finds in space. On Earth she chooses a spring and attaches a rock to it that weighs 20 N. After placing the rock on a horizontal table, and attaching the spring horizontally to a fixed point, she stretches the rock 2 cm from equilibrium, in the positive direction. She then releases it from rest. After 30 s has passed, she finds that the rock has gone through 10 cycles and is at a new positive maximum value, which is 1 cm from equilibrium. (a) What is the period of the oscillation? (b) What is the spring constant of the spring? (c) What is the time constant of the decay? (d) Find a function that describes the motion, including damping, of the spring and mass system that is only a function of time. Assume time starts when the mass is released. (e) Roughly sketch (1) the position vs time and (2) velocity vs time of this setup. (f) Later, during the return from a mission on Mars (no gravity), she wants to know the mass of an unknown rock she’s found. This rock is attached to the same spring, which is now attached to the wall of the spacecraft. The mass is disturbed from equilibrium and the period of the resulting oscillations is found to be 2 s. What is the ratio of the mass of the new rock to the mass of the rock found on Earth?

Astronomy:

6.What is a brown dwarf? Is it different from a proto-star? How?

7. What different types of gas do astronomers find in the interstellar medium?

8. Astronomers believe the Sun formed with other stars near the Orion Nebula. If that is true, why is the Sun here and not there?

9. Astronomers can tell the age of a star by the age of its cluster. How is this determined?