Explain why gravitational lensing is not a great way to discover large numbers of extrasolar planets given our current resources and technology. Also explain how, if you were determined and had access to enormous funding resources, you could still use gravitational lensing to discover a significant number of extrasolar planets. Conditions: you cannot leave the Earth’s surface, take an unlimitted amount of time, or send anything out from Earth to achieve your goal.

A)

A mass weighing 16 pounds stretches a spring 8/3 feet. The mass is initially released from rest from a point 4 feet below the equilibrium position, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 1/2 the instantaneous velocity. Find the equation of motion x(t) if the mass id riven by an external force equal to f(t) = 20 cos 3t use g=32 ft/s^2 for the acceleration due to gravity)

B)

A mass of 1 slug, when attached to a spring stretches it 2 feet and then comes to rest in the equilibrium position starting at t=0 an external force equal to f(t)=6 sin 4t is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. use g=32 ft/s^2 for the acceleration due to gravity.

Suppose a sinusoidal wave on a string, having amplitude A and travelling in the −xˆ direction, is partially reflected at the point x = 0, so that the reflected wave is in phase with the incident wave at x = 0 but has amplitude kA, where 0 ≤ k ≤ 1 is the reflection coefficient. a) Show that each point on the string undergoes simple harmonic motion and determine how the amplitude of the simple harmonic motion varies with x b) Find the ratio of maximum to minimum amplitude, known as the standing wave ratio

I need rapport about Waves and (difine ,types, equation ,conditions )of the waves and explain what's the different between wave phase velocity and group velocity...use good handwritten ...report not less than 3 pages..

A tennis ball is it at ground level. The ball reaches its maximum height above the ground level 1 sec. after being hit. Then 0.9 seconds after reaching its maximum height, the ball barely clears the net that is 3 m from where the tennis ball was hit. Assume the ground is level. How high is the net?  How far beyond the net does the tennis ball strike the ground?

How would you know define one to one correspondence when talking with the parents?

2/ when we say that the eight official IAU planets have orderly motions, what do we mean?

A/ we mean that they all orbit the Sun in the same big circle, all in a line, one after the other, all revolving counterclockwise

B/ we mean that they orbit the Sun in nearly circular orbits, all going clockwise, all in the same plane

C/ we mean that they orbit the Sun in nearly circular orbits, all going counterclockwise, all in the same plane

D/ we mean that they orbit the Sun in a sphere, all going counterclockwise

5/ where in the solar nebula did rentals condense, in all likelihood?

A/ only outside the frost line

B/ only inside the frost line

C/ it never got cold enough in the solar nebular for metals to condense

D/ everywhere throughout the solar nebula, except very close to the Sun

6/ what, in all likelihood, is the primary reason for the separation of planetary properties (roc/metal-rich vs gas-rich) with distance from the Sun in our Solar System?

A/ scientists can’t explain this observation

B/ the location of the frost line in the Solar Nebula and the types of materials which were able to condense within or outside that line

C/ the location of the bombardment line in the solar nebula and where a planetesimal was located relative to that line

D/ how quickly the solar wind was able to reach the planet to turn off hydrogen and helium gas accretion

7/ Imagine that instead of being between the orbits of Mars and Jupiter, the frost line had instead been located at about Earth’s orbit. What impact might that have had on the number of terrestrial planets in our solar system?

A/ the location of the frost line had nothing to do with the formation of the planet

B/ the number of terrestrial planets would probably have gone down.

C/ there would probably have been no impact

D/ the number of terrestrial would have gone up

8/ why do scientists think did the Jovian planets stop growing?

A/ once a Jovian planet reaches Jupiter’s size, feedback mechanisms in its accretion disk prevent further growth

B/ the solar wind blew the remaining gas away, preventing further growth by accretion gas

C/ they naturally stopped growing once they had accreted all of the gas in the solar nebula

D/ all of the hydrogen compounds and rock/metal condensates beyond the frost line destroyed themselves in collisions, so they could not collide with Jovian planet planetesimals and make them grow

9/ imagine that the solar wind had turned on later in the formation of the solar system than it did. What impact might that have had on the growth of the planets?

A/ planetary formation would have been extended, and planets would have ended up being bigger than they are

B/ planetary formation would have been interrupted and planets would have ended up being smaller than they are

C/ there would have been no impact

13/ 4 planets orbit 4 identical stars. All 4 planets orbit their parent stars at identical average distances. The planets are all terrestrial-type planets, and range in size from small to very large. Which planet would you expect to be the most geologically active?

A/ the rockiest planet

B/ the biggest planet

C/ a planet which is smaller than the biggest planet, but larger than the smallest planet

D/ the smallest planet

14/ Consider what would have happened to a large (~10 times the mass of the Earth) planetesimal if it had formed beyond the orbit of Neptune. If that planetesimal had gone on to form a planet, how would you expect that planet’s mass to compare to the mass of Saturn

A/ larger mass than Saturn

B/ similar to our Sun

C/ smaller mass than Saturn

D/ same as Saturn

15/ which Jovian planet has the biggest internal pressure?

A/ Jupiter

B/ Neptune

C/ Uranus

D/ Saturn

16/ which Jovian planets, if any, have cores which are differentiated into a layer of hydrogen compounds and a layer of rock and metal?

A/ Jupiter

B/ Saturn

C/ Uranus

D/ neptune

E/ all of the above

F/ only Jupiter and Saturn

G/ only Uranus and Neptune

H/ none

17/ why is Io more volcanically active than our moon?

A/ Io is still warm from its formation process

B/ Io is much larger than our moon

C/ Io has a different internal heat source

D/ Io has a higher concentration of radioactive elements

A car driver has rear ended a truck but claims he was driving the speed limit before hitting the brakes. The driver left a 50m long streak of tire rubber when he slammed on the brakes. The mass of the drivers car is 1000kg. The coefficient of friction between the tire and asphalt is 0.5. The mass of the truck that got hit is 5000kg. The speed limit for the road is 40mph. What was the magnitude of the acceleration of the car? (Remember that magnitudes are always positive). How fast was the car going right before the driver slammed on the brakes?

A) List two reasons (other than the expected errors in the dimension meaurements) why your measured value for the density of steel may differ from the accepted value

B) List two reasons that might explain any percent difference between the two values for the density of copper.

Prove that (cos x + isin x) n = cos nx + isin nx. (Hint: Use Euler’s formula).

A student working in the physics laboratory connects a parallel-plate capacitor to a battery, so that the potential difference between the plates is 225 V. Assume a plate separation of d = 1.27 cm and a plate area of A = 25.0 cm². When the battery is removed, the capacitor is plunged into a container of distilled water. Assume distilled water is an insulator with a dielectric constant of 80.0.

(a) Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes.)

before Q_i = ___ pC

after Q_f = ___ pC

(b)

Determine the capacitance (in F) and potential difference (in V) after immersion.

C_f = ___ F

ΔV_f = ___ V

(c) Determine the change in energy (in nJ) of the capacitor.

ΔU = ___ nJ

(d)

What If? Repeat parts (a) through (c) of the problem in the case that the capacitor is immersed in distilled water while still connected to the 225 V potential difference.

Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes.)

before Q_i = ___ pC

after Q_f = ___ pC

Determine the capacitance (in F) and potential difference (in V) after immersion.

C_f = ___ F

ΔV_f = ___ V

Determine the change in energy (in nJ) of the capacitor.

ΔU = ___ nJ

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.) )