After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth. (a) Calculate the average density of the white dwarf.

(b) Calculate the surface free-fall acceleration

(c) Calculate the gravitational potential energy associated with a 2.04-kg object at the surface of the white dwarf.

A space station has a large ring-like component that rotates to simulate gravity for the crew. This ring has a mass M = 2.1×10^5 kg

and a radius of R= 86.0 m and can be modeled as a thin hoop. Before spinning up the ring section, crew members Dave and Frank

dock their ships, each with mass m= 3.5×10^4 kg on two docking ports located on opposite sides of the center of the ring. The docking

ports are located r = 31.0 m from the center of the ring. When the station’s computer begins to spin up the ring it has to spin both the

ring and the ships. The ships can be treated as point particles. Two identical thrusters on the edge of the ring are used to spin up the

ring with a constant angular acceleration. The ring-ship system takes 3 hours to reach the angular speed at which it simulates Earth’s

gravity for the crew on the edge of the ring. What constant force must each of the two thrusters apply to reach this rotational speed?

#1 A microwave oven has a power requirement of 1,261 W. A frozen dinner requires 4.1 min to heat on full power.

(a) How much electrical energy (in kWh) is used?
_________kWh

(b) If the cost of electricity is 13¢ per kWh, how much does it cost to heat the dinner? (Do not round your final answer. Fractional cent values are acceptable.)
______________¢

#2 - A student who weighs 556 N climbs a stairway (vertical height of 2.6 m) in 23 s.

(a) How much work is done?
__________J

(b) What is the power output of the student?
__________W

In a neutron scattering experiment, a neutron scatters off the stationary nucleus of an atom with an atomic mass of 61 amu in a 1 dimensional, elastic collision. After the collision, what percentage of the neutron's kinetic energy was transferred to the atom? In a second neutron absorbtion experiment, a neutron is absorbed into the nucleus of an atom with an atomic mass of 62 amu. After the collision, what percentage of the neutron's kinetic energy was remains?

Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg. This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles.

a) If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the  α particles after they are released?

b) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the slower-moving α particle after it is released? Assume that the α particles move entirely in the x-direction.

c) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the faster-moving α particle after it is released?  Assume that the α particles move entirely in the x-direction.

I have to do an experiment/ demonstration for my PHY251 class (Calculus based physics). I am only allowed to do it on one of the following topics: Vectors, Accelerated motion, Centripetal force, Free fall, projectile motion, Inertia, Equilibrium, Friction, Orbits, Tides. Does anyone have any ideas for a cool demonstration? Please provide instructions for the demonstration/experiment. Thank you in advance.

M, a solid cylinder (M=1.71 kg, R=0.133 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.690 kg mass, i.e., F = 6.769 N. Calculate the angular acceleration of the cylinder.

5.95×10¹ rad/s^2

If instead of the force F an actual mass m = 0.690 kg is hung from the string, find the angular acceleration of the cylinder.

How far does m travel downward between 0.730 s and 0.930 s after the motion begins?

The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.379 m in a time of 0.470 s. Find I_cm of the new cylinder.

Write a 6-7 on how the ‘theory’ for projectile motion of the ‘stream of water’, (i.e., many small water particles), may useful to design a fountain.

Compare (take the ratio) the rate of heat conduction through a 20.0-cm-thick wall that has an area of 10.0 m2 and a thermal conductivity twice that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of 2.00 m2, assuming the same temperature difference across each. Show a few steps. Qualitatively, explain how you can reduce heat conduction through a window in winter.

A 10?? object hangs from a rope. The charge of the object is 30 ??. The object hangs 0.5 ? above a charge of −20 ?? on the floor

a) Find the tension in the rope.

d) Find the new tension in the rope if the ground were 20 ?? instead of −20 ??.

Explain What steps you are taking also please

A white billiard ball with mass m_w = 1.33 kg is moving directly to the right with a speed of v = 2.96 m/s and collides elastically with a black billiard ball with the same mass m_b = 1.33 kg that is initially at rest. The two collide elastically and the white ball ends up moving at an angle above the horizontal of ?_w = 29

You have three charged conducting spheres. The magnitude of these charges are 4C, 5C and 6C. Without knowing which charges are positive and which charges are negative, which of the following could represent the charge on a single sphere if the spheres are brought into contact with each other and then separated?

a. -10 C

b. 15 C

c. 0.5 C

d. -1 C

A monatomic ideal gas is at an initial pressure of 1.54 atm and 76.0 cm3. The gas undergoes an isochoric increase in pressure to 2.31 atm, then an isobaric expansion to 114 cm3. Pressure is reduced isochorically to the original pressure before an isobaric compression returns the gas to its initial values. For 1.95 moles of the gas, complete the following:

a) Generate a sketch of the PV diagram, with values clearly represented.

b) Find the heat absorbed and heat rejected during each cycle.

c) Find the work done in one cycle. d) Calculate the efficiency of the heat engine.

e) Determine the minimum and maximum temperatures during the cycle.

f) Calculate the Carnot efficiency of the heat engine.

g) Find the maximum work that can be done by a Carnot engine that absorbs heat found in part b.

h) Determine the coefficient of performance of a Carnot refrigerator operating between the temperature found earlier.

i) Determine the coefficient of performance of the system if operated as a heat pump.

1) The curl of gradient = 0
2) The divergence of curl = 0

I know how to prove these mathematically but can you explain me with a physical example or interpretation as why it is zero? Like I want to know the intuition.