You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630 km above the planet's surface, the ship's orbital speed is 5500 m/s . By observing the planet, you determine its radius to be 4.48×10^6 m. You then land on the surface and, at a place where the ground is level, launch a small projectile with initial speed 13.6 m/s at an angle of 30.8∘ above the horizontal. If resistance due to the planet's atmosphere is negligible, what is the horizontal range of the projectile? Please explain process

What is the current thinking on the little hierarchy problem in light of a potential Higgs mass above 120 GeV? A few years ago, at least, I remember various phenomenologists saying that this at least makes life rather difficult for the MSSM.

Goldstein's Classical Mechanics has a puzzling few sentences in his discussion of orbits.

Referring to the case of orbit where the energy is low enough for the orbit to be bounded, he says :"This does not necessarily mean that the orbits are closed. All that can be said is that they are bounded, contained between two circles of radii r1 and r2 with turning points always lying on the circles."

Doesn't "bounded" automatically mean "closed"? The object cannot escape from the attractive force and hence returns over and over. At least, that is my understanding of the terms. Wikipedia says "The orbit can be open (so the object never returns) or closed (returning), depending on the total energy (kinetic + potential energy) of the system." But it also says "Orbiting bodies in closed orbits repeat their paths after a constant period of time." So the only way out I see is if a closed orbit is a special case of non-precessing bounded orbit.

A simple generator has a square armature 7.0cm on a side. The armature has 95 turns of 0.59-mm-diameter copper wire and rotates in a 0.800-T magnetic field. The generator is used to power a lightbulb rated at 12.0 V and 25.0 W. At what rate should the generator rotate to provide 12.0 V to the bulb? Consider the resistance of the wire on the armature.

Consider the work-energy theorem relating work done on an object and its change in kinetic energy. What is the formula? Explain in your own words what this formula gives you. Create an example. Include a graphical or picture representation that illustrates what all the variables are. Then exemplify the use of the formula with a simple problem of your own creation. The problem should be stated in words first. Every variable should have a well defined value with appropriate units. Finally, solve your problem.
( please show image and explain clearly)

A person walks into a room and switches on the ceiling fan. The fan accelerates with constant angular acceleration for 18s until it reaches its operating angular speed of 2.0rotations/s - after that its speed remains constant as long as the switch is "on". The person stays in the room for a short time; then, 5.5 minutes after turning the fan on, she switches it off again and leaves the room. The fan now decelerates with constant angular acceleration, taking 2.4 minutes to come to rest.

What is the total number of revolutions made by the fan, from the time it was turned on until the time it stopped?

Express your answer using two significant figures.

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 1.993 10-26 kg and 2.159 10-26 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 7.88 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8400 T.

Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

Straws work on the principle of the outside atmospheric pressure pushing the fluid (for example water) up the straw after you have lowered the pressure at the top of the straw (in your mouth). Assuming you could create a perfect vacuum in your mouth, what is the longest vertical straw you could drink water from?

1.65 m

4.28 m

7.71 m

10.3 m

8)  How would this answer change if you were on a planet with a much lower atmospheric pressure?

increases

decreases

remains the same

9)  A block of wood (density 550 kg/m³) and a block of metal (density 2700 kg/m³) with equal volume are placed 1 m under water in a swimming pool. Which has a greater buoyant force on it?

the metal

the wood

they have the same buoyant force

10)  Which has a greater force of gravity on it?

the metal

the wood

they have the same force of gravity

11)  Compare the buoyant force to the force of gravity for each object.

In both cases the buoyant force is greater.

In both cases the force of gravity is greater.

For the metal, the buoyant force is greater; for the wood, the force of gravity is greater.

For the wood, the buoyant force is greater; for the metal, the force of gravity is greater.

12)  If they were taken to a depth of 10 m what would happen to the buoyant force on each (assume the density of water is constant and the objects are incompressible)?

they increase

they decrease

they remain the same

13)  If the objects were connected together, would they sink or float?

they would sink

they would float

they would stay right where the are!

14)  Water is flowing through a pipe that slowly gets smaller as it rises to the bathroom on your second floor (10 m high). The pipe coming into your house is 3 cm in diameter, the pressure there is 3x10⁵ Pa, and the water is moving at .8 m/s. The diameter of the pipe in the upstairs bathroom is 1.5 cm. How fast is the water moving right before it leaves the pipe in the bathroom?

.2 m/s

.4 m/s

1.6 m/s

3.2 m/s

15)  What is the pressure of the water in the pipe right before it leaves the pipe?

1.50x10⁵ Pa

1.97x10⁵ Pa

2.88x10⁵ Pa

3.67x10⁵ Pa

Given the vectors A= 2.00i + 6.00j and B= 3.00i - 2.00j, (a) draw the vector sum C= A + B and the vector difference D = A - B. (b) Calculate C and D in terms of unit vectors. (c) Calculate C and D in terms of polar coordinates, with angles measured in respect to the positive x-axis.

Baked potatoes are normally wrapped in aluminum foil. How does this affect the cooling of the potato after it is removed from the oven? (Consider radiation)

A road with a radius of 72 m is banked so that a car can navigate the curve at a speed of 13 m/s without any friction. When a car is going 25 m/s on this curve, what minimum coefficient of static friction is needed if the car is to navigate the curve without slipping?

A room with 2.7-m-high ceilings has a metal plate on the floor with V = 0V and a separate metal plate on the ceiling. A 1.5 g glass ball charged to 5.0 nC is shot straight up at 4.7 m/s .

How high does the ball go if the ceiling voltage is 2.9×10⁶ V ?

How high does the ball go if the ceiling voltage is −2.9×10⁶ V ?

A rescue helicopter lifts a 70.6-kg person straight up by means of a cable. The person has an upward acceleration of 0.728 m/s² and is lifted from rest through a distance of 11.5 m. (a) What is the tension in the cable? How much work is done by (b) the tension in the cable and (c) the person's weight? (d) Use the work-energy theorem and find the final speed of the person.

An electron is accelerated inside a parallel plate capacitor. The electron leaves the negative plate with a negligible initial velocity and then after the acceleration it hits the positive plate with a final velocity β. The distance between the plates is 11.0 cm, and the voltage difference is 147 kV. Determine the final velocity β of the electron using classical mechanics. (The rest mass of the electron is 9.11×10^-31 kg, the rest energy of the electron is 511 keV.)

What is the final velocity β of the electron if you use relativistic mechanics?