. It is often said that “water seeks its level.” Explain

A bumper car with mass m₁ = 122 kg is moving to the right with a velocity of v₁ = 4.5 m/s. A second bumper car with mass m₂ = 2m₁ = 244 kg is at rest. The two have an elastic collision and the first bumper car rebounds backwards at a speed that is 1/3 of its original speed (1.5 m/s). Assume the surface is frictionless.

1) What is the change in momentum of bumper car 1? (let the positive direction be to the right)

2) What is the change in momentum of BOTH bumper cars combined?

3) What is the change in momentum of bumper car 2?

4) What is the final velocity of car 2?

5) What is the change in energy of bumper car 1?

6) What is the change in energy of BOTH bumper cars combined?

7) What is the change in energy of bumper car 2?

7.15 Channel equalization. We suppose that u1, . . . , um is a signal (time series) that is trans- mitted (for example by radio). A receiver receives the signal y = c ∗ u, where the n-vector c is called the channel impulse response. In most applications n is small, e.g., under 10, and m is much larger. An equalizer is a k-vector h that satisfies h∗c ≈ e1, the first unit vector of length n + k − 1. The receiver equalizes the received signal y by convolving it with the equalizer to obtain z = h ∗ y.

(a) How are z (the equalized received signal) and u (the original transmitted signal) related? Hint. Recall that h∗(c∗u) = (h∗c)∗u.

(b) Numerical example. Generate a signal u of length m = 50, with each entry a random value that is either −1 or +1. Plot u and y = c ∗ u, with c = (1,0.7,−0.3). Also plot the equalized signal z = h ∗ y, with

h = (0.9, −0.5, 0.5, −0.4, 0.3, −0.3, 0.2, −0.1).

propagate errors for magnitude and theta.

magnitude(aka R) = sqrt(Rx²+Ry²)

tetha = arctan(Ry/Rx)

unclear on how to get the equation delta R and delta theta.

In an insulating box, there is a 140.0g block of lead whose temperature is 100K and a 70.0g block of tungsten whose temperature is 300K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the system between the initial and the equilibrium state? (c) What is the change in the entropy of the system? (specific heat of tungsten: 0.0321cal/g · K, molar specific heat of tungsten: 24.8J/mol · K, specific heat of lead: 0.0305cal/g ·K, molar specific heat of lead: 26.5J/mol·K

Question regarding moles:

So I'm having a hard time understanding the relationship between moles, molar mass, atomic/molecular mass, and unified atomic mass units.

Is molar mass and atomic/molecular mass the same thing? It seems like atomic/molecular mass is the sum of all the atomic masses in a substance. The units for atomic/molecular mass is unified atomic units and the units for molar mass is g/moles, so it seems like some type of conversion is happening. A Helium atom has an atomic mass of 4.00 u and a molar mass of 4.00 g/mol. So is 1 u = 1 g/mol? Doesn't that go against the idea that 1 u = 1.66 * 10^-27 kg? I can see that 1g/ mol = 10^-3 kg/mol, but how do you get rid of the mol part? Is it using the notion that in 1mole of gas there are 6.022 * 10^23 molecules to get that conversion because 1.66 * 10^-27 kg needs to equal 1 g/mol if 1g/mol = 1u?

Also physically, what is the difference between the mass of the substance and the atomic/molecular mass? If the substance is just the mass of everything it contains wouldn't that be the same thing as adding up all the molecules making that substance? I'm also assuming that the atomic/molecular mass is the actual mass of the atom or molecule itself, is that the case? Or is it like the mass of the nucleus of each atom (molecular mass would then be the sum of all the masses of all the nuclei). In that case, then the atomic mass doesnt include the mass of the electrons thus creating a difference between the actual mass of the substance and the atomic/molecular mass.

Explanation of reasons why wireless electricity and energy harvesting could cut waste and reduce greenhouse gas emissions.

What sort of exoplanets are the easiest target for direct imaging, and why?

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?