Diffraction grating produces its third-order bright band at an angle of 79.4 ∘ for light of wavelength 791 nm .

Part A

Find the number of slits per centimeter for the grating.

n = 

Part B

Find the angular location of the first-order bright band.

θ1 = 

Part C

Find the angular location of the second-order bright band.

θ2 = 

Part D

Will there be a fourth-order bright band?

A stone with a weight of 5.25 N is launched vertically from ground level with an initial speed of 19.0 m/s, and the air drag on it is 0.261 N throughout the flight. What are (a) the maximum height reached by the stone and (b) its speed just before it hits the ground?

A copper block is removed from a 299

The Mars Reconnaissance Orbiter (launched on 8/12/2005) achieved a nearly circular orbit in September 2006 with a period of T = 6.72 x 10³ s. The mass, M, of Mars is 6.417 x 10²³ kg and its radius, R_Mars, is 3.39 x 10⁶ m.

The mass, m, of the Orbiter is 1,031 kg.

1) The Net Radial Force, ΣF_r, acting on the Orbiter as it orbits Mars, is due to the gravitational force between it and Mars. ΣF_r = GMm/r², where r is the orbital radius.

True or False

2) This Net Radial Force, ΣF_r, is also equal to mv²/r = m(2π/T)²r.

True or False

3) Accordingly, r = [GM(T/2π)²]^1/3

True or False

4) The speed, v, and the radius, r, of the Orbiter depend on the Orbiter's mass.

True or False

5) The Orbiter is _____x 10⁶ m from the center of Mars. Show your answer with the correct number of significant figures.

True or False

6) How many times does the Orbiter circle Mars in one earth day? (Show three significant figures in your answer. Don't try to use exponential notation. Use numbers like 3.76 or 15.9)

7) The value of g, gravitational acceleration, near the surface of Mars is ______ m/s².

8) An engineer is planning to put another satellite around Mars with a radius of r = 4.000 x 10⁷ m. Its speed in m/s would be:

9) What is the period, T, of the above planned satellite in earth days (to 2 significant figures)?

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