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.

1. Which of the following would not be observed if you observed the sky without a telescope? (More than one answer can be correct).

Venus moves relative to the Sun.

Mars moves relative to the stars.

The starts rotate about a single point in the sky.

The stars move relative to each other.

The Moon moves relative to the stars.

2.Comparing theories by Ptolemy and by Copernicus. (More than one answer may be correct)

A ball of mass m is attached to a string of length L. It is swung in a vertical circle with enough speed to keep the string taut throughout the motion. Assume the ball travels freely in the circle with negligible loss of mechanical energy. Determine if the following six statements are true or false; e.g., enter TTFFFF.

1. 
   
2. The tension in the string is less at the top of the circle than at the bottom of the circle.
3. The acceleration of the ball at the bottom of the circle is directed `down'.
4. mv_b²/L = T_b−mg, where v_b and T_b are the speed of the ball and the tension of the string at the bottom of the circle.
5. The speed of the ball at the bottom of the circle is greater than the speed at the top of the circle.
6. The tensions at the top and at the bottom of the circle depend on the average speed of the ball.
7. The tension in the string at the top of the circle is always greater than the weight of the ball.

If I want to design an experiment related to kinetic friction, can the following proposal meet the requirement?
By varying the weight of an object and measure the stopping distance of that object.
Is this related to kinetic friction? If not, how should I change my experiment?

A cylindrical air tank has dimensions diameter = 0.2m and height 0.8m. an attached pressure gage reads 200 kPa and the temperature is 27 celcius. an electrical heater is energized inside and it raises the temperature to 147 celius in 2 minutes. Calculate the mass of air in the tank (kg) (have to use ideal gas law, molecular weight of air)

n = 4.33 mol of Hydrogen gas is initially at T = 378 K temperature and pi = 2.88

A 4.50 kg solid cylinder with radius 10.0 cm is allowed to roll down a uniform slope that has been inclined at 22°. The cylinder is stationary at the top and the length of the incline is 5.50 meters.

1. What percentage of the total KE is rotational KE at the bottom of the ramp?

2. What is the angular acceleration of the cylinder as it rolls down the ramp?

3. Find the velocity of the cylinder at the bottom of the ramp.

4. What is the net torque applied to the rolling cylinder during its motion down the ramp?

A 1,300-N crate is being pushed across a level floor at a constant speed by a force F of 390 N at an angle of 20.0° below the horizontal, as shown in the figure a below. Two figures show a side view of a crate positioned upon a horizontal surface. Figure (a): An arrow pointing downward and to the right is labeled vector F and forms an angle of 20° below the horizontal as it approaches the upper left edge of the crate. Figure (b): An arrow pointing upward and to the right is labeled vector F and forms an angle of 20° above the horizontal as it extends from the upper right edge of the crate.

(a) What is the coefficient of kinetic friction between the crate and the floor? (Enter your answer to at least three decimal places.)

0.256 Correct: Your answer is correct.

(b) If the 390-N force is instead pulling the block at an angle of 20.0° above the horizontal, as shown in the figure b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a).

0.7 Incorrect: Your answer is incorrect.

6. Given the Earth's albedo of A = 0.3, what surface temperature do you predict at equilibrium? Is this consistent with the Earth's actual average temperature of 14C? How do you explain the discrepancy?

A 1094 kg van, stopped at a traffic light, is hit directly in the rear by a 727 kg car traveling with a velocity of +2.41 m/s. Assume that the transmission of the van is in neutral, the brakes are not being applied, and the collision is elastic. What is the final velocity of the car?