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Ok, first, I'll give the problem, then my solutions and how I got stuck.... Be aware that this is a long question, though.

An green hoop with mass Mh = 2.6 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass Md = 2 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat horizontal surface that rolls without slipping and has mass Ms = 4.2 kg and radius Rs = 0.19 m. The system is released from rest.

1)What is magnitude of the linear acceleration of the hoop?

2)What is magnitude of the linear acceleration of the sphere?

3)What is the magnitude of the angular acceleration of the disk pulley?

4)What is the magnitude of the angular acceleration of the sphere?

5)What is the tension in the string between the sphere and disk pulley?

6)What is the tension in the string between the hoop and disk pulley?

7)The green hoop falls a distance d = 1.68 m. (After being released from rest.)

How much time does the hoop take to fall 1.68 m?

8)What is the magnitude of the velocity of the green hoop after it has dropped 1.68 m?

9)What is the magnitude of the final angular speed of the orange sphere (after the green hoop has fallen the 1.68 m)?

Ok, so here's my approach:

1) I set up the system between the hoop and the pulley such that the torque is equal:

Rd*(Mh*a - T) = I*alpha, where I is (1/2)*Md*Rd^2

Rd*Mh*a - Rd*T = (1/2)*Md*Rd^2*(a/Rd)

The Rd's cancel out, leaving

Mh*a - T = (1/2)*Md*a

So now I have to find T. So I set a similar equation to the sphere and the pulley, giving me:

Rd*T = I*alpha, where I = (1/2)*Md*Rd^2

Solving for this gives me T = (1/2)*Md*a

However, plugging this back into the previous equation gives me that a = 0.... which can't be right....

So can someone tell me what I did wrong?

As for the rest of the 8 questions.... They're not difficult as long as I have the linear acceleration.

2) I'm assuming linear acceleration is the same for the whole system, so if I got the answer for #1, then it should be the same answer for this question.

3) It should be the linear acceleration divided by the radius of the disk/pulley due to the equation

a = alpha*R. Again, I need the answer from #1.

4) Same idea as #3, except using the radius of the sphere.

5) If I know the linear acceleration, then finding the tension using the equation from #1 shouldn't be bad.

6) I'm guessing same as #5. Correct me if I'm wrong.

7) Not so bad using linear kinematics. As long as I know the distance and linear acceleration.

8) Again, using linear kinematics like #7.

9) Using rotational kinematics, this question shouldn't be too bad.

I don't want a detailed plan/outline for this. But I'm confused when the essay asked me to evaluate the cultural significance. What does this generally ask for?

Does it mean I should take past cultural histories related to that performance and compare it to the actual performance? Or does it mean I should literally look at possible cultural aspects that were seen during the performance and relate it to past cultural histories? I'm just a bit confused on what it's asking for.

Thanks.

Here's the question:

A mixture of yellow light (wavelength = 582 nm in vacuum) and violet light (wavelength = 404 nm in vacuum) falls perpendicularly on a film of gasoline that is floating on a puddle of water. For both wavelengths, the refractive index of gasoline is n = 1.40 and that of water is n = 1.33. What is the minimum nonzero thickness of the film in a spot that looks the color of violet and yellow because of destructive interference?

I do not get this at all. It looks really complicated and I know it's easy to solve if you set your mind to it.... but I just can't get it. Can someone describe how to start it out and tell me the answer that he or she got so I can confirm that what I did was correct?

Ok, here's question 1:

Light of wavelength 625 nm (in vacuum) is incident perpendicularly on a soap film (assume n = 1.33) suspended in the air. What are the two smallest nonzero film thicknesses (in nm) for which the reflected light undergoes constructive interference?

I know that the wavelength of the film would be 625/1.33. But after that, shouldn't this be the first smallest? I know it's not, but why? And how can you get the second smallest wavelength?

So the problem goes like this:

An object is located 13.5 cm in front of a convex mirror, the image being 7.35 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

I know that the magnification equation is involved, but the thing is that it seems to contradict.

m = hi/ho = -di/do

Based on the problem, the convex mirror's magnification is 7.35/13.5 = 49/90. However, in the other situation, the convex mirros's magnification is 2, which contradicts the 1st magnification.

Can someone tell me what I did wrong and how to solve it please?

I don't really get this one:

Determine the power dissipated in the 7.0 resistor in the circuit shown in the drawing. (R1 = 3.0 , R2 = 7.0 and V1 = 16 V.)

I can't really copy the diagram, but it's a complete circuit with a resistor in series with resistors in parallel. So basically, the circuit first goes to resistor R1 then travels trhough a parallel circuit of two lines, one of which is a resistor of 3 ohms while the othe line contains R2 and another resistor of 1 ohm. Then it reconnects and goes back to the battery.

I can easily get the current here, but how do I find the power of R2 since the voltage would be different and the current might be different as well?

I gave each problem a try before, but I got both wrong (most likely due to that I misunderstood something).

So anyways, here's the first problem:

One heater uses 340 W of power when connected by itself to a battery. Another heater uses 235 W of power when connected by itself to the same battery. How much total power do the heaters use when they are both connected in series across the battery?

Unless if it's just me, P = (I^2)(R). And since the current is the same with resistors in a series, the only thing interchangeable is the resistance. Therefore to find the total power, I just add them together to find the toal power. But what did I do wrong?

Second question:

Two resistors have resistances R1 and R2. When the resistors are connected in series to a 14.0 V battery, the current from the battery is 2.00 A. When the resistors are connected in parallel to the battery the total current from the battery is 9.00 A. Determine R1 and R2. (Assume R1 is the smaller of the two resistances.)

Okay, so I got 2 equations: 14 = 2 (R1 + R2) and 9 = 14 ((R1 + R2)/(R1xR2)) with the former being the equation for the resistors being in series and the latter being the resistors in parallel. I just can't seem to use these two to find R1 or R2. Can someone explain how to do this one?

Here's the question:

A lamp is placed in series with a resistor and a 120.0 V source. If the voltage across the lamp is 30 V and the power which it dissipates is 50.0 W, what is the resistance R of the resistor?

Why is there two different type of voltage? I'm sort of lost. =(

There was a question that asked to prove tan40 as something else by using only Demovire's Theorem [(rcis theta)^n = (r^n cis theta)]. However, I can't seem to convert tan40 into a cis form.

Can someone explain how to convert it into cis form?

The question goes like this:

Point A is at a potential of +210 V, and point B is at a potential of -140 V. An α-particle is a helium nucleus that contains two protons and two neutrons; the neutrons are electrically neutral. An α-particle starts from rest at A and accelerates toward B. When the α-particle arrives at B, what kinetic energy (in electron volts) does it have?

I think this has to do with the concept of Total Energy, but could someone explain how I would apply it to find kinetic energy in terms of electron volts? Do I just find the work that was done and then convert it to electron volts?

Here's the question:

Suppose that the electric potential outside a living cell is higher than that inside the cell by 0.079 V. How much work is done by the electric force when a sodium ion (charge = +e) moves from the outside to the inside? Please answer in J.

I don't undertsand how this works from the textbook, so can someone explain it to me? It said something about Electric Potential Energy, but I don't know how to find the Electric Potential Energy. Either that, or I forgot.

What happens to those who lost their jobs when a new type of communication took place? For example, like those people who link telephone calls. Once email came in, telephone isn't needed as much anymore. So what happened to them after they lost their jobs? Or another example is when the radio got replaced by television. There are some people who can speak very well in the radio, but when it comes to television, they don't look so great. What happens to them? How do they cope with this?

If you even have a related fact that doesn't seem to be so significant, tell me. I'd like to learn all of the history because it interests me greatly.

H2 is a gas. However, when it makes contact with fire, it creates a popping sound and the fire distinguishes. What exactly happened during that reaction?

HCl (aq) and Mg (solid) combined to form H2 and something else. I got something like 2HCl + Mg ===> H2(g) +MgCl2. But I'm unsure if that's correct or not. Can someone explain the correct molecular equation and the net ionic equation?

If HCl (in an aqueous solution) is combined with CaCO3 (solid), then what's the net ionic equation. Sorry if this seems like a lot to do. I know that CO2 is produced, but I can't get it....

And if you possibly can, please explain how it's done...

I understand that larger rackets has more power, but shouldn't a bigger racket also mean that it should be a bit easier to also have more control like making spins (because there's a bigger area)? Could someone explain it in a simple way?

I want to improve my speed and jumping abilites by at least a bit in another 7 or 8 months. I considered ankle weights or weight vests, but I'm not so sure after researching the affects. Does anyone have suggestions or strategies for how to improve without weights?