1. [13 marks total]

   1. (a) [1] Suppose on the Moon, a meteoroid creates a crater in the shape of a hemisphere with a radius of 1 km.

      Calculate the mass of material excavated, assuming a density of 1920 kg/m3 for regolith.

   2. (b) [1]When the meteoroid makes the crater,the excavated material is raised vertically by a distance equal to the

      radius of the crater, 1 km. Calculate the potential energy required to lift the material.

   3. (c) [3] The meteoroid that created the crater was spherical and made of rock, and it had an impact velocity of

      5 km/s. Assuming that energy was conserved in the collision, what was the size of the meteoroid?

   4. (d) [5] Comets have a density of one third the value of rocky meteoroids, but can travel three times as fast. If a comet the same size of the meteoroid had impacted and caused the crater, with a density of 1000 kg/m3 and an impact velocity of 15 km/s, what size crater would have been made? Would it be larger or smaller than that made by a rocky meteoroid?

   5. (e) [3] Consider the material excavated by the impactor, the ejecta. Ejecta blankets are found on both Mercury and the Moon, but on Mercury, the ejecta is generally much closer to the crater compared to the Moon. Explain why this is.

Efficiency

An ideal diatomic gas is used in a reversible heat cycle. The gas begins in state A with pressure 100 kPa, temperature300 K, and volume 0.50 L. It first undergoes an isochoric heating to state B with temperature 900 K. That is followed by an isothermal expansion to state C. Finally, an isobaric compression that returns the gas to state A.

(a)Determine the pressure, volume, and temperature of state B.

(b)Determine the pressure, volume, and temperature of state C.

(c)Compute the work and heat exchanged with the gas going from state A to B.

(d)Compute the work and heat exchanged with the gas going from state B to C.

(e)Compute the work and heat exchanged with the gas going from state C to A.

(f)Compute the efficiency of the heat cycle.

A block with a mass M is attached to a horizontal spring with a spring constant k. Then attached to this block is a pendulum with a very light string holding a mass m attached to it. What are the two equations of motion? (b) What would these equations be if we assumed small x and φ? (Do note that these equations will turn out a little messy, and in fact, the two equations involve both variables (i.e. they are coupled.) )

Show by direct computation that the impulse momentum theorem and the work-energy theorem are invariant under the Galilei transformation.

Three point charges, q, 2q, and 3q, are at the vertices of an equilateral triangle of sides a. If q= 15.8 nC and a= 11.1 cm, what is the magnitude of the electric field at the geometric center of the triangle?

Please explain in details, in particular the trig to set up the equilateral triangle. I am confused.

A 2000-kg car is traveling at 20 m/s on a horizontal road and the engine suddenly is broken down. The brakes immediately are applied and the car skids to a stop in 4.0 s with a constant acceleration because of kinetic friction. What is the coefficient of kinetic friction between the tires and road?

Why was it unnecessary to connect the ground alligator clip in the Oscilloscope experiment

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.658 of the escape speed from Earth and (b) its initial kinetic energy is 0.658 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth?

Consider a finite square well, with V = 1.2 eV outside. It holds several energy states, but we are only interested in two:

• E₁ = 1.15 eV
• E₂ = 1.1 eV

1) For E = 1.15 eV, what is the decay constant, κ, outside the well in nm^-1(i.e., where V = 1.2 eV)?

κ =

2) For E = 1.1 eV, what is the decay constant, κ, outside the well in nm^-1 (i.e.,) where V = 1.2 eV)?

κ =

3) For E = 1.15 eV, suppose the probability density at some position,x, outside the well is P(x) and the probability density 1 nm farther from the well is P(x+1 nm). What is the ratio, P(x+1 nm)/P(x), of these two probailities?

Ratio =

4) For E = 1.1 eV, suppose the probability density at some position,x, outside the well is P(x) and the probability density 1 nm farther from the well is P(x+1 nm). What is the ratio, P(x+1 nm)/P(x), of these two probailities?

Ratio =

5) If we squeeze the well (decrease L), the energies of the states will increase. What is the limiting value κ_limit of an energy state's κ as its energy approaches the top of the well in nm^-1(i.e., as E → 1.2 eV).

κ_limit =

Question 2: You want to determine if there are any Kuiper Belt objects larger than Eris.

Part a: Describe the observational methods and analysis you would apply to search for them.

Part b: How might you determine if any candidate objects are larger than Eris? What observational data do you need for an object to estimate its radius?