an Astronomy question, please answer it comprehensively. Thank you

List (and explain) two reasons astronomers suspect that Dark Matter exists.

Question 1

A 242 g box slides up a 16.1° ramp at a speed of 4.05 m/s. Using conservation of energy and assuming the ramp is frictionless, how far along the ramp does the box slide before stopping?

0.745 m
3.02 m
29.6 m
0.871 m

Question 2

A 10800 kg jet is preparing to land on a military aircraft carrier. In order to do so, the pilot manoeuvres the jet's tail to hook and snag a cable that is attached to a spring with spring constant 71200 N/m. If the spring stretches 33.0 m to stop the jet, what was the jet's landing speed?

218 m/s
14.7 m/s
84.7 m/s
120. m/s

Question 3

You are lawn bowling and bowl a ball with a speed of 5.23 m/s. Unfortunately, your ball hits a large rock of mass 310 g, resulting in a perfectly elastic collision. If the final velocity of the ball after the collision is -2.42 m/s, what must the mass of the ball be?

0.114 kg
0.844 kg
0.424 kg
1.18 kg

The sound intensity is 0.0072 W/m2 at a distance of 20 m from an isotropic point source of sound. (a) What is the power of the source? (b) What is the sound intensity 6.1 m from the source? (c) What is the sound level 20 m from the source?

A photon of wavelength 6.63 pm scatters at an angle of 167 ∘ from an initially stationary, unbound electron. What is the de Broglie wavelength of the electron after the photon has been scattered?

An ideal monatomic gas originally at a pressure of 3x10⁵ Pascals and 75 moles and volume 1.2 m³ & T_i is expanded isothermally to a volume of 3.5 m³ at which point it has pressure P₁. It then experiences an isovolumic process to a lower pressure P₂, T₂. Finally, it is compressed adiabatically back to its original state and returns to its original pressure, temperature, and volume.

Find:

T_i , P₁ , P₂ , T₂

ΔE_{1 of gas}, ΔE_{2 of gas} , ΔE_{3 of gas} , ΔE_{Total of gas}

W_{1by gas}, W_{2 by gas}, W_{3 by gas}, W_{Total by gas}

Q_{1 into gas}, Q_{2 into gas}, Q_{3 into gas}, Q_{Total into gas}

_{Answers should be:}

Ti = 577.62 Kelvin, P1 = 102,857.14 Pascals, P2 = 50,206.54 Pascals, T2 = 281.95 Kelvin

ΔE1 of gas = 0 Joules, ΔE2 of gas = -276.41 kJoules, ΔE3 of gas = 276.41 kJoules, ΔETot of gas = 0 Joules

W1 by gas = 385.36 kJoules, W2 by gas = 0 Joules, W3 by gas = -276.41 kJoules, WTot by gas = 108.95 kJoules

Q1 into gas = 385.36 kJoules, Q2 into gas = -276.41 kJoules, Q3 into gas = 0 Joules, QTot into gas = 108.95 kJoules

A cockroach of mass m lies on the rim of a uniform disk of mass 4.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.230 rad/s. Then the cockroach walks half way to the center of the disk.

What then is the angular velocity of the cockroach-disk system? What is the ratio K/K₀ of the new kinetic energy of the system to its initial kinetic energy? What accounts for the change in the kinetic energy?

How to combine the point-particle and real system/extended system analyses of a system to compute changes in the system’s internal energy?

A uniform disk with mass 8.5 kg and radius 8 m is pivoted at its center about a horizontal, frictionless axle that is stationary. The disk is initially at rest, and then a constant force 31.5N is applied to the rim of the disk. The force direction makes an angle of 35 degrees with the tangent to the rim. What is the magnitude v of the tangential velocity of a point on the rim of the disk after the disk has turned through 8.1 revolutions? The unit of the tangential velocity is m/s.

Consider the following. (a) Find the angle θ locating the first minimum in the Fraunhofer diffraction pattern of a single slit of width 0.186 mm, using light of wavelength 424 nm. (b) Find the angle locating the second minimum.

Problem 3

The purpose of this problem is to find the Net Magnetic Field force of the two electric currents at point P.

There are two parallel wires carrying currents I₁ = 15 A and I₂ =25 A, as it is shown in the figure below. The arrow on each wire shows the direction of the current in the wire.

The distance between the two wires is 10 Cm. The distance between point P and the wire (I₁ ) on the left is 4 Cm.

1 Cm = 10^-2 m

Instruction:

            Solid blue circle indicates the direction of the electric current is out of the paper

         Solid blue circle with a cross sign indicates the direction of the electric current goes in to the paper.

I₁ = 15.0 A (solid blue) -------------------pX-------------------------------------------------------(solid blue w/cross) I₂ = 25.0

1. Calculate the magnetic field ( B1) of the left wire (I ₁ ) at point P. Show your formula and solution below this line.

B1 =

2. Calculate the magnetic field ( B2) of the right wire (I ₂ ) at point P. Show your formula and solution below this line.

B2 =

3. Draw the magnetic field vectors B1 and B2,   at point P, on the figure.

4. Calculate the net magnitude of the magnetic field , B(Net) and show the direction of the B(Net) at that point (P).

Three identical stars of mass M form an equilateral triangle that rotates around the triangle’s center as the stars move in a common circle about that center. The triangle has edge length L. What is the speed of the stars? b.) What is the period of revolution? c.) What is the total potential energy of the 3 star system? Express your answers in terms of the star mass M and triangle edge length L. Hint: Draw a diagram showing the gravitational forces on each star. d.) Find the gravitational force on a single star due to the gravitational attraction of the other two stars, (magnitude and direction). Hints: the 2nd law for a single particle orbiting a planet i.e. Fg = M v 2 /R. You will need to express R in terms of the triangle edge length L. Use v T = 2πR to find the period. it is a symbols-only problem. All work must be done in symbols. There are no numbers.

10. Water at a pressure of 3.60 atm at street level flows into an office building at a speed of 0.60 m/s through a pipe 4.40 cm in diameter. The pipes taper down to 1.50 cm in diameter by the top floor, 23.0 m above. Calculate the water pressure in such a pipe on the top floor.

A 0.478 kg puck, initially at rest on a horizontal, frictionless surface, is struck by a 0.129 kg puck moving initially along the x axis with a speed of 2.19 m/s. After the collision, the 0.129 kg puck has a speed of 1.19 m/s at an angle of 29◦ to the positive x axis. Determine the magnitude of the velocity of the 0.478 kg puck after the collision. Answer in units of m/s.

The mass of a hot-air balloon and its cargo (not including the air inside) is 220 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 490 m³. To what temperature must the air in the balloon be warmed before the balloon will lift off? (Air density at 10.0°C is 1.244 kg/m³.)
K