1) Because of the mass involved in constructing and transporting a lander, the first human expedition to Mars will likely be an orbital mission. A geosynchronous orbit seems plausible, allowing astronauts in the spacecraft to have continuous line-of-sight control of rovers on the surface. What is the altitude above the surface of Mars for geosynchronous orbit? You’ll need to do some research to find the mass of Mars and its rotation period.

2) Using the expression for the escape velocity from a planet.
a) Describe the physics that went into your derivation of the escape velocity and list the formula again.
b) Use this formula to calculate the escape velocity of Mars and compare it with Earth. List the sources where you obtained the properties of each planet for your calculation.
c) What insight might you glean from the above calculation on why Mars has a thinner atmosphere than the Earth?

3) Assuming that the outer planets (Saturn, Uranus, and Neptune) are in equilibrium with the solar radiation, calculate the effective surface temperature of these 3 planets and show all intermediate steps. You can assume albedos of 0.5, 0.6, and 0.6, for Saturn, Uranus, and Neptune, respectively. The solar luminosity is 3.83 x 1026 W. How do these temperatures compare with their observed temperatures?

A shell is launched at angle 62° above the horizontal with initial speed 30 m/s. It follows a typical projectile-motion trajectory, but at the top of the trajectory, it explodes into two pieces of equal mass. One fragment has speed 0 m/s immediately after the explosion, and falls to the ground. How far from the launch-point does the other fragment land, assuming level terrain and negligible air resistance?

how might a sonogram tech encounter heat, heat transfer, and/or thermal expansion?

Bubba (m=100kg) and Sally (m=60kg) are playing on a merry-go-round. Treat the merry-go-round as a disk with mass 100 kg and radius 1.3 m. Both Bubba and Salley are at the edge of the disk when the disk is rotating at .25 revolutions per second. Suppse Bubba moves inward so that he is now exactly at the center. Treat the two children as point masses. Assuming there is no external torques or forces,

A) What is the new rotational speed of the merry-go-round?

B) How much work is done? Who, what did this work?

Ice at −14.0 °C and steam at 142 °C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0 °C is present. Ignoring the container and the equilibrium vapor pressure of the liquid, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg.C°).

A point charge with a mass of 1.81 ng and a charge of +1.22 ?C moves in the x-y plane with a velocity of 3.00 x 104 m/s in a direction 15° above the +x-axis. At time t=0, the point charge enters a uniform magnetic field of strength 1.25 T that points in the +x-direction.Assume that the point charge remains immersed in the uniform magnetic field after time t=0.

a) What is the magnitude and direction of the magnetic force that the magnetic field exerts on the point charge at time t=0?

b) How does the x-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

c) How does the y-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

d) Use your answers from parts 1b & 1c to explain why the path of this point charge is helical (corkscrew-shaped). Explain your reasoning.

e) Determine the radius of the circular part of the point charge’s helical path.

A torque of 36.2 N · m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 9.5 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 60.2 s later.

A- What is the wheel's moment of inertia

B- What is the magnitude of the torque caused by friction

C- From the time the directed force is initially applied, how many revolutions does the wheel go through?

A cart of mass m1 = 5.69 kg and initial speed = 3.17 m/s collides head-on with a second cart of mass m2 = 3.76 kg, initially at rest. Assuming that the collision is perfectly elastic, find the speed of cart m2 after the collision.

A bullet flies horizontally, hits a wooden block suspended from a 1.0 m string, and gets stuck in the block. The angle of deviation of the string equals 11 degrees. The mass of the bullet is 1000 times smaller than the mass of the block. What is the initial speed of the bullet? Point out the laws of physics in the solution and show all steps.

A 5.1 cm diameter horizontal pipe gradually narrows to 2.5 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 35.0 kPa and 21.8 kPa , respectively. What is the volume rate of flow?

A transverse wave propagates in a very long wire of mass per unit length 4 x 10^3 kg/m and under tension of 360 N. An observer next to the wire notices 10 wave peaks (or 'crests') passing her in a time of 2 seconds moving to the left.

a. If at t = 0 and x = 0 the displacement assumes its maximum value of 1 mm, what is the explicit equation for the wave?

b. Calculate the maximum longitudinal velocity for a infinitesimal segment of the wire (a 'particle' on the wire if you like)?

Now assume the same wire has been fixed on both ends so that the two fixed points are separated by unknown length L. The tension remains the same. One of the resonance frequencies of the wire is 375 Hz. The next higher resonance frequency is 450 Hz.

c. What is the fundamental frequency of the string?

1. Engineers are designing a rocket to be used in deep space. If the rocket is fired from rest in deep space, the total mass of the rocket, payload, and unspent fuel must reach a speed of 1.10 ✕ 10⁴ m/s in order to accomplish other maneuvers. Due to the amount of fuel which is still onboard, the rocket, payload, and unspent fuel will have a final mass of 4.10 ✕ 10³ kg. If the design of the rocket is such that the exhaust speed is 2.55 ✕ 10³ m/s, determine the amount of fuel required to perform this maneuver.

2. A 51.0 kg astronaut has been spacewalking outside her spacecraft and realizes that she is stranded (stationary) a distance of d = 15.0 m from the outside of the spacecraft. In order to get back, she throws a 1.25 kg hammer directly away from the ship. If the spacecraft is a sphere with a 2.00 m radius, determine the distance of the hammer from the outside of the ship when she reaches the safety of the ship.

3. An ice skater with a mass of 51.0 kg is gliding across a smooth lake with a speed of 2.05 m/s when she hits a spot of ice covered with snow. After a time of 7.65 s she has slowed to a stop. Using your knowledge of momentum, determine the magnitude of the average force of friction acting on the ice skater while she slows to a stop.

You are pushing a sled in which your little sister is seated up a 26° slope (one that makes an angle of 26° with the horizontal). If the mass of the sled and girl is 46 kg, and the coefficient of kinetic friction between the sled and the surface is 0.100, with what force (in N) do you need to push in order for the sled to move with constant velocity?