Part A

Calculate the magnitude of the angular momentum of the Earth in a circular orbit around the sun. The Earth has mass 5.97

A 300,000 kg- spacecraft is floating in space when it senses a 40-kg enemy missile coming toward it at 20m/s. The spacecraft fires at 60 kg lump of clay at 30m/s directly at the missile. The clay sticks to the missile. (a.) Show that the spacecraft recoils at about 6mm/s (1mm=0.001m) (b.) Show that the final velocity of the clay-laden missile is 10 m/s in a direction away from the spacecraft.

You are on an engineering team examining the feasibility of a satellite launching system that uses the electric force instead of rocket fuel. The proposed launching system consists of 4 metal spheres, each one 15 m above the ground, arranged at the corners of a square with sides 5 meters long. The satellite is placed on the ground below the center of the square. To launch the satellite, the four spheres are first each given a charge of +Q/4 and the satellite is given a charge –Q. The satellite is then released and is pulled straight upward through the center of the square.

When the satellite reaches 15 m above the ground (the same height as the spheres), the spheres are neutralized. To evaluate this idea, you decide to calculate how big Q would have to be to launch a 100 kg satellite at a speed of 8 km/s. You are also worried about dielectric breakdown of the air, which causes spontaneous sparking in the presence of electric fields larger than 3 x 10⁶ V/m and so decide to check whether that will be a problem. For this purpose, you assume that the spheres have a diameter of 1 m.

(a) Give a purely symbolic answer to the problem in terms of (only) the quantities given in the problem and known constants. Be sure to define each of the symbols you use.
(b) Give a numerical answer to the problem.

How do you find the total internal reflection angle? I know that if the incident angle is larger than the critical angle, that will lead to total internal reflection. So is it just a concept (like there no degree/ angle/ numerical value given to total internal reflection)? Thank you!!

A dye molecule has electrons that are free to travel up and down a chain of atoms, giving electron energy states that are given by the particle-in-a-box model, with En=(0.34eV)n2. What are the three longest wavelengths of visible light that the molecule will absorb?

In simple terms (so a non-physicist with an upper division math background can understand), what is a Lagrangian and what is it used for?

Ampere's Law for a long wire states that magnetic field is directly proportional to current and inversely proportional to the distance for the wire. True or False.

Ampere's Law for a loop wire states that magnetic field is indirectly proportional to current and directly proportional to the radius of the loop. True or False.

Ohm's Law is true regardless of the nature of the electric circuit. True or False

Thank you!

Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in (Figure 1) If each internal resistance is r = 0.400? , and R = 4.00 ?, what is the voltage across the resistor R?

An object moving in a circle at a constant speed has no acceleration.

True or false.

Marc is in no way athletic, never goes to the gym, and gets winded by just walking up some stairs. When he was in his undergrad, Marc used to be late for the bus frequently. One time, he was running at 5 m/s to catch a bus that he was late for while the bus was 40 m away. Marc then noticed the bus started to drive away with a constant acceleration of a = 0.17 m/s^2 (Marc can notice these things).

1. (a) How long does Marc have to continuing running at 5 m/s to catch the bus? How much distance has he covered in that time?

2. (b) When Marc reaches the bus, how fast is the bus traveling?

3. (c) You may have noticed that the mathematical process in part (a) produces two solutions. Explain the physical meaning of the second solution. How fast is the bus traveling at this point?

4. (d) Now, it’s a miracle Marc was able to even achieve a speed of 5 m/s. In all honesty, he can likely only reach 3.5 m/s (at best). At this speed, would Marc catch the bus?

5. (e) What is the minimum speed someone would need to be able to run to catch the bus under these conditions? What would be their running time be and total distance traveled?

what is the maximum efficiency of a solar cell? recall the temperature of the sun is 5600 K.

A helium balloon ride lifts up passengers in a basket. Assume the density of air is 1.28 kg/m³ and the density of helium in the balloon is 0.18 kg/m³. The radius of the balloon (when filled) is R = 5.4 m. The total mass of the empty balloon and basket is m_b = 122 kg and the total volume is V_b = 0.064 m³. Assume the average person that gets into the balloon has a mass m_p = 73 kg and volume V_p = 0.079 m³.

1) What is the volume of helium in the balloon when fully inflated?

m³

2) What is the magnitude of the force of gravity on the entire system (but with no people)? Include the mass of the balloon, basket, and helium.

N

3) What is the magnitude of the buoyant force on the entire system (but with no people)? Include the volume of the balloon, basket, and helium.

N

4) What is the magnitude of the force of gravity on each person?

N

5) What is the magnitude of the buoyant force on each person?

N

6) How many FULL people can the balloon lift up? (Your answer must be an integer.)

people

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3. A car with mass 1200 kg travels at 35 m/s, while a second car with mass 1500 kg travels at 25 m/s. The two cars collide in a perfectly inelastic collision.

a) What is the final velocity (speed and direction) if the first car was travelling north and the second travelling south?   
b) If the first car were travelling north and the second were travelling east?

4. Sam stands on a 4-m-long hanging scaffold suspended by two ropes, one at either end.

a) If Sam has a mass of 80 kg, and the scaffold has a mass of 40 kg, what is the minimum tension that could be felt by a single rope if the system is in static equilibrium?
b) What is the maximum tension that could be felt by a single rope if the system is in static equilibrium?

Calculus-based physics rotational inertia:

a) Two disks are mounted (like a merry-go-round) on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. The first disk, with rotational inertia 2.56 kg·m² about its central axis, is set spinning counterclockwise (which may be taken as the positive direction) at 309 rev/min. The second disk, with rotational inertia 7.07 kg·m² about its central axis, is set spinning counterclockwise at 760 rev/min. They then couple together. (a) What is their angular speed after coupling? If instead the second disk is set spinning clockwise at 760 rev/min, what are their (b) angular velocity (using the correct sign for direction) and (c) direction of rotation after they couple together?

b) The uniform rod (length 0.309 m) in the figure rotates in the plane of the figure about an axis through one end, with a rotational inertia of 0.275 kg·m². As the rod swings through its lowest position, it collides with a 0.242 kg putty wad that sticks to the end of the rod. If the rod's angular speed just before the collision is 3.21 rad/s, what is the angular speed of the rod-putty system immediately after the collision?

1. Suppose rain falls vertically into an open cart rolling along a straight horizontal track with negligible friction. As a result of the accumlating water, the kinetic energy of the cart.

a. increases
b. does not change
c. decrease

2. two marbles, one twice as heavy as the other, are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has

a. as much kinetic energy as the lighter one
b. twice as much kinetic energy as the lighter one
c. half as much kinetic energy as the lighter one
d. four times as much kinetic energy as the lighter one
e. impossible to determine

3. A person attempts to knock down a large wooden bowling pin by throwing a ball at it. The person has two balls of equal size and mass, one made of rubber and the other of putty. The rubber ball bounces back, while the ball of putty sticks to the pin. Which ball is most likely to topple the bowling pin?

a. the rubber ball
b. the ball of putty
c. makes no difference

4. We launch a 1 kg block with spring along a rough surface (coefficient of kinetic friction of 0.45).
a.If a spring compression of 0.25m launches the block a total of 2.5m, what is the spring constant of the spring?
b.How much compression is required to reach a target 5.0m away?