Spring Kinematics and Electricity/magnetism properties.

[Plutoman]

To give some starting info, these are intro questions to my AP Physics course I'm taking.

I was able to solve all but these fairly easily - these eluded me as to how to start solving the problem, essentially with the conceptual idea behind it in the first one, and a lack of basic understanding due to no teachings in the ideas of magnetism and resistivity.

11. Block A of mass 2.0kg and block B of mass 8.0 kg are connected as shown above by a spring of spring constant 80 N/m and negligible mass. The system is being pulled to the right across a horizontal frictionless surface by a horizontal force of 4.0N, as shown, with both blocks experiencing equal constant acceleration.

http://img389.imageshack.us/img389/8096/loldrawingbx5.png

a) Calculate the force that the spring exerts on the 2.0kg block.
b) Calculate the extension of the spring.

The system is now pulled to the left, with the 4.0N force pulling the smaller block first, and the spring connecting this to the larger block. Both blocks again experience equal constant acceleration.

c) Is the magnitude of the acceleration greater than, less than, or the same as before?
d) Is the amount the spring has stretched greater than, less than, or the same as before?
e) In a new situation, the blocks and the spring are moving together at a constant speed of 0.5 m/s to the left. Block A then hits and sticks to a wall. Calculate the maximum compression of the spring.

12. A rectangular wire loop is connected across a power supply with an internal resistance of 0.50 Ohms and an emf of 16v. The wire has resistivity of 1.7 * 10^-8 Ohm-meters and cross sectional area 3.5 * 10^-9 m^2. When the power supply is turned on, the current in the wire is 4.0 Amps.
a) Calculate the length of wire used to make the loop.

The wire loop is then used in an experiment to measure the strength of the magnetic field between the poles of a magnet. The magnet is placed on a digital balance, and the wire loop is held fixed between the poles of the magnet, as shown below. The 0.020m long horizontal section of the loop is midway between the poles and perpendicular to the direction of the magnetic field. The power supply in the loop is turned on, so that the 4.0A current is in the direction shown.

http://img389.imageshack.us/img389/9215/seconddrawingjj4.png

b) In which segment is the force on the magnet due to the current in the wire segment? Upward or Downward?

Justify your answer.

c) The reading on the balance changed by 0.060N when the power supply was turned on. Calculate the strength of the magnetic field.

In the first problem - I wasn't sure how the force was transferred through the spring. Would, since each block is subject to the same acceleration, the force applied on the 2.0kg block be 1/4th of the 8.0kg block? And from that - a 1N force, using the simple equation of F = -kx, would the distance stretched be correspondingly equal to 1/80th of a meter?

For the second portion - since the forces are equal, just reversed, the blocks should be subject to the same acceleration. Am I correct there? I've kinda lost myself theoretically in the rest of it - it may be due to a lack of sleep, or I could just be doing this whole section wrong. If someone can point me to how the system works conceptually, I can do the work easily - I'm just lost there.

In the second problem, I have no concept of resistivity and magnetism, nor how to calculate these values. If someone could point me in the direction of equations to use, some conceptual information either here or a link to a site, it would be much appreciated.

Btw: These are custom paint drawings imitating what was on the page, so the quality isn't great and it's not nearly to scale by any means, but it gives a moderate representation. And the problems are typed word for word.

Thanks in advance for any help :)

 

[Gear300]

Interestingly, these were the questions for the 2007-2008 exam (the most recently tested one).

To start the first one off...4N is being applied to a system of a total mass of 10kg. The acceleration of the system is simply a = F/M, F being the external force of 4N and M being the total mass of the system. The entire system shares the same acceleration and so the 2kg mass is moving at that acceleration. Use that to find the spring force being exerted on the mass and the extension of the spring. Using what you found for (a) and (b), it should be able to hint for the other parts.

For the second one...for part (b)...its as simple as equal and opposite forces (Newton's 3rd Law)...but for the direction and the rest of the question...well...if you're not knowledgeable of the concept of electromagnetism...then fully understanding the problem will not be as easy. Is your instructor expecting you to have actual answers or is he just testing how much you already know?

 

[Plutoman]

Ahh, yep, I see for the first problem. I'm not doing the math atm, but I can work it out fairly easily from here on.

The second one... I think he's kind of expecting us to find help - i.e., something like this - and to test our knowledge.

Out of 13 problems, he said he would be extremely surprised and would definitely be expecting a full easy 5 on the AP test if anyone got a straight up score of over 90%.

So, he's expecting us to either not know or not remember it all - I'd love too, if possible, be able to learn some of this and surprise him though :P

Would you know of any resources I could look at?

I'm vaguely familiar with some of it - but much evades me. I tend to learn fast, though (I don't always keep it with me for a long while... that only comes with lots of repeated use...), and I feel that I would like to be able to make the attempt at the problem. As it is, I have no concept of what equations to use nor how any of it works out.

Edit: And the AP exam is likely where he got them from - he said they were AP questions, I wasn't sure if it meant it was from a particular AP test - or just AP style, but apparently it was the former.