1. Dark Energy

(a) Why is dark energy "dark"? Why is it "energy"?

(b) Give at least one way that dark energy is different from dark matter. Also give at least one way that dark energy is similar to dark matter.

(c) What is the difference between the cosmological constant and dark energy?

Jake asked Sally to draw a vector perpendicular to the vector 4.0i - 6.0j +2.0k. Which vector would Sally draw?

A) 1.0i-2.0j+1.0k B) 2.0i -3.0j +1.0k C) 2.0i+1.0k D) 1.0i +1.0j+1.0k E) 3.0i -3.0j+3.0k

A train car with mass m1 = 576 kg is moving to the right with a speed of v1 = 7 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at vf = 4.4 m/s.

A)What is the initial momentum of the first train car?
B)What is the mass of the second train car?
C)What is the change in kinetic energy of the two train system during the collision?
D)Now the same two cars are involved in a second collision. The first car is again moving to the right with a speed of v₁ = 7 m/s and collides with the second train car that is now moving to the left with a velocity v₂ = -5.1 m/s before the collision. The two cars latch together at impact.

What is the final velocity of the two-car system? (A positive velocity means the two train cars move to the right – a negative velocity means the two train cars move to the left.)

An object 0.800 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 20.5 cm.

A:

Calculate the position of the image.

Express your answer in centimeters to three significant figures.

s'=?

B.

Calculate the size of the image.

Express your answer in centimeters to three significant figures.

'y'= ?

C.

Find the orientation (upright or inverted) and the nature (real or virtual) of the image.

Options:

upright and real

upright and virtual

inverted and real

inverted and virtual

Water is flowing in the pipe shown in the figure below, with the 7.70-cm diameter at point 1 tapering to 3.45 cm at point 2, located y = 11.5 cm below point 1. The water pressure at point 1 is 3.20 ✕ 104 Pa and decreases by 50% at point 2. Assume steady, ideal flow. What is the speed of the water at the following points? Point 1? Point 2?

A disk of radius 14 cm and has a mass of 10 kg is attached to a hub which is a
disk of mass 8 kg and radius 5cm. The disks are mounted on a frictionless axel
that runs through the center. A rope passes over the hub and supports a 10 kg
mass on one side and a 5 kg mass on the other. If the rope does not slip on the
hub,
a.) What is the tension in the segment of the rope that has the 10 kg mass
b.) What is the torque on the rope above the 5 kg mass?
c.) What is the angular acceleration?
d.) What is the velocity of the 10 kg mass after it has fallen 30 cm?

Calculate the magnitude of the electric potential difference across the length

9. A stainless steel tube having an outside diameter of 0.6 cm and a wall thickness of 0.05 cm is to be insulated with a material having a thermal conductivity of 0.065 W/mK. If the inner and outer convective heat transfer coefficients are 5.9 W/m²K. what will be the heat loss per meter of length for insulation thicknesses of 0, 0.25, 0.5, 0.75, 1.00, and 1.25 cm if the inside temperature is 95 C and the outside temperature is 10 C? Plot heat loss per meter versus insulation thickness. Also, plot the surface and interface temperatures as a function of insulation thickness.

a) DERIVE the equation for the change in the free energy of a CYLINDRICAL nucleus heterogeneously forming from an existing phase. The nucleus grows with its circular base on

the mold wall and the axis of the cylinder normal to the wall. ASSUME that the height of the cylinder can be written as h = a * r, where a is a constant, and r is the cylinder radius.

b) Find the critical radius and the energy barrier to nucleation for this shape of precipitate.

c) We can vary the shape of the nucleating phase by changing the constant a. Make a log- log plot of the size of the energy barrier versus the parameter a over a range from a

= 0.01 (disk shaped) to a = 100 (needle shaped). Explain your results.

Dark matter; C&O 24.22.

(a) Assume that the density of dark matter in our Galaxy is given by ρ(r) = ρ0/(1+(r/a) ^2) . Show that the amount of dark matter interior to a radius r is given by: Mr = 4πρ0a^2 [ r − a tan^−1 ( r/a )].

(b) If 5.4 × 10^11 M⊙ of dark matter is located within 50 kpc of the Galactic centre, determine ρ0 in units of M⊙ kpc−1 . Repeat your calculation if 1.9 × 10^12 M⊙ is located within 230 kpc of the Galactic centre. Assume that a = 2.8 kpc.

Suppose that you decided to send a spacecraft to Neptune using a Hohmann transfer. The craft starts in a circular orbit close to the Earth (1 AU) and is to end up in a circular orbit near   Neptune (about 30 AU).   (a) How long would the transfer take?   (b) How could you shorten this time, without increasing the amount of fuel required?   (c) What change in velocity is needed to enter the transfer orbit?   (d)   What is the change in velocity needed to enter the circular orbit near Neptune?

SCENERIO: You are working for a humanitarian aid agency that plans to air-drop supplies into a war-torn region. The political landscape is such that in order to reach the civilians in need – and not fall into the wrong hands – the supplies must land in a very precise location. The agency’s helicopters are equipped with a ramp down which bundles of supplies can be rolled as a means of launching them. The bundles of supplies are spherical and cylindrical, and come in a variety of sizes and masses. Enough friction is present on the ramp that all bundles are certain to roll without slipping as they are launched. It is up to you to determine from where on the ramp each bundle of supplies should be launched, assuming the helicopter hovers at a constant height.

QUESTION: Now assume that conditions in the war-torn region have deteriorated to the point that it is no longer safe for a helicopter to hover stationary above the ground for a supply drop. How would your answers about where to drop supplies change if they are instead released from an aircraft moving with constant velocity? With constant acceleration?

Compare the green house effect on Earth to Venus then discuss two similarities and two differences in the green house effect between Earth and Venus.

Indicate whether each quantity increases, decreases, or remains the same for the situation being described: The number of particles and volume are held constant and the gas is cooled