A hollow cylindrical container has an inner radius of 7.3040 cm as stated from the manufacturer. The height of container is measured to be 20.50 cm. The thickness of the container walls can be neglected. For each part, round the final answer to the correct number of significant figures. a) Calculate the volume of this cylinder with the correct number of significant figures and units of . b) The container is filled to the top with water. The water molecules are approximated to be spheres with a diameter of 2.75 angstroms. Estimate to within one order of magnitude how many water molecules are present inside of the container. c) If the density of water is 1,000.0 kg/ , determine the mass of the water inside of the container. d) Two numbers, each having two significant figures, are added together. Is it possible for the sum to have three significant figures? Show an example and explain.

In the diagram, the dashed lines are parallel to the x axis. The magnitudes of the vectors are A = 8.8, B = 6.8, C = 13.5, D = 21.9, and F = 21.9. The angles, in degrees, are θ_A = 30.0, θ_B = 53.0, θ_C = 60.0, θ_D = 37.0, and θ_F = 30.0. In this problem, you will be asked to calculate the value of a variety of scalar (dot) products.

a) What is A • C?

b) What is A • F?

c) What is D • C?

d) What is A • (F + 2C)?

e) What is i • B?

f) What is j • B?

g) What is (3i - j) • B?

h) What is (B/B) • B?

A sports car of mass 1000 kg can accelerate from rest to 72. km/h in 6.6 s.
a) What would the average force of the car's engine be?
b) If the same force acts on 2000 kg car what is the acceleration.

Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 3.0 cm -tall object is 15 cm in front of the 40 cm -focal-length lens. Calculate the image height.

A thin film of soap solution (n = 1.33) has air on either side and is illuminated normally with white light. Interference minima are visible in the reflected light only at wavelengths of 480, 520, and 1040 nm in air.

What is the minimum thickness of the film? (Express your answer to two significant figures.)

The figure below (Figure 1) illustrates an Atwood's machine. Let the masses of blocks A and B be 3.50 kg and 2.00 kg, respectively, the moment of inertia of the wheel about its axis be 0.400 kg⋅m2 and the radius of the wheel be 0.130 m.

Part A

Find the linear acceleration of block A if there is no slipping between the cord and the surface of the wheel.

Express your answer in meters per second squared.

Part B

Find the linear acceleration of block B if there is no slipping between the cord and the surface of the wheel.

Express your answer in meters per second squared.

Part C

Find the angular acceleration of the wheel C if there is no slipping between the cord and the surface of the wheel.

Express your answer in radians per second squared.

Part D

Find the tension in left side of the cord if there is no slipping between the cord and the surface of the wheel.

Express your answer in newtons.

Part E

Find the tension in right side of the cord if there is no slipping between the cord and the surface of the wheel.

Express your answer in newtons.

Please answer all parts. Will leave a thumbs up and a positive comment for correct and full answer.

Thank you!

4) A proton is suspended in the air by an electric field where the acceleration due to gravity is g. What is the strength of this electric field?

2) What is the value of the electric field .5 m from a square piece of metal which is 1 km x 1 km and has a net charge of 1 C?

A peanut sits 8.0 cm away from the center of a turntable that is spinning at a rate of 200 rad/s. If it takes 15.0 s from the turntable to come to a stop at a constant rate, what is the direction relative to the vertical of the force exerted on the peanut by the turntable 14.7 s after the turntable has begun slowing down? With a diagram if possible.

One mole of an ideal gas undergoes a process where the pressure varies according to

P = (-17.0 atm/m⁶) V² + (32.5 atm/m³) V + 1.80 atm

where V is the volume. The volume initially starts at 0.0265 m³ and ends at a value of 1.05 m³.

1. Generate an accurate P-V graph for this situation.
2. Determine the initial and final temperatures for this situation.
3. Determine the change in internal energy for this situation.
4. Determine the work done for this situation.
5. Determine if any work was added or removed for this process.
6. Is the process adiabatic?

Thermodynamics and Statistical Mechanics Problem:

1. You have just microwaved a cup of tea for too long and it is boiling, too hot to drink. You look around and see a punchbowl containing ice floating in water. You thoroughly mix one cup of water (no ice) from the punchbowl with your cup of tea in a thermos bottle. What is the change in entropy of the pint of liquid? Does the sign of the change make sense? Explain.

A cylindrical copper rod of length 1.60 m and cross-sectional area 7.10 cm^2 is insulated to prevent heat loss through its surface. The ends are maintained at a temperature difference of 100 degrees C by having one end in a water-ice mixture and the other in boiling water and steam. Find the rate at which ice melts at one end (in grams/second).

Define center of mass of a system of three particles. If the particles are of different masses, how will the center of mass of the system move, explain

A circular conducting loop of radius 25.0 cm is located in a region of homogeneous magnetic field of magnitude 0.300 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 283 Ω. The magnetic field is now increased at a constant rate by a factor of 2.80 in 19.0s.
Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

Calculate the magnitude of the current induced in the loop while the field is increasing.

With the magnetic field held constant at its new value of 0.84 T, calculate the magnitude of the average induced voltage in the loop while it is pulled horizontally out of the magnetic field region during a time interval of 8.30 s