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  1. D

    Representing a Cardioid

    Homework Statement Show that the cardioid r=a(1+cos(theta)) can be represented by r=2acos2(theta/2), 0<=theta<=2pi (theta is between 0 and 2pi). Homework Equations The Attempt at a Solution I'm pretty sure I have to equate the two expressions, but I haven't been able to do this...
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    Electric Potential Energy of a System of Charges

    Oh I see...that makes sense. You're right, I was counting each interaction twice. I worked on the problem again and got (4+sqrt(2))kQ2/a...can anyone confirm this?
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    Electric Potential Energy of a System of Charges

    Woops sorry, the line that says U = (8+sqrt(8)kQ2)/a is supposed to say: U = ((8+sqrt(8))kQ2)/a
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    Electric Potential Energy of a System of Charges

    Homework Statement A square of side a has a charge +Q at each corner. What is the electric potential energy of this system of charges? Express your answer in terms of the variables a, Q and appropriate constants. Homework Equations U=kq1q2/r The Attempt at a Solution I figured...
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    Energy Conservation - Electric Potential Energy

    Oh I see...my calculator didn't show me those last few digits. Thanks so much for your help!
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    Energy Conservation - Electric Potential Energy

    I don't quite understand what I've done wrong. I did the calculation again and I'm still getting 7.0x10^-9 C. I'm assuming the units of C are correct since the division yields Joules/Volt, and Joule = Coulomb * Volt. I also checked over my conversion of MV to V and that is correct as well.
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    Energy Conservation - Electric Potential Energy

    Homework Statement In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor’s DNA, thus killing its cells. For one patient, it is desired that 0.10 J of proton energy be...
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    Setting up an Integral for the area of a surface of revolution

    oops, i meant to put a "*" for multiplication. Thanks for your help!
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    Setting up an Integral for the area of a surface of revolution

    So does this mean that the way I have set it up is correct? I had a feeling it wasn't right because I couldn't see what steps I'd take next in the event that I had to solve it.
  10. D

    Setting up an Integral for the area of a surface of revolution

    Homework Statement Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve y=xe-x 1=<x=<3 about the y-axis. Homework Equations S=integral from a to b x 2pix ds where ds=sqrt(1+(dy/dx)2)dx The Attempt at a Solution The first thing I...
  11. D

    Walking away from two loudspeakers-destructive interference

    I just thought of something...would I use n=1 and then n=0 to find the other 2 values?
  12. D

    Walking away from two loudspeakers-destructive interference

    Ok, I solved it the way you said and everything worked out :) The only problem is that they're asking for three values...how would I find the other 2?
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    Walking away from two loudspeakers-destructive interference

    I see. So now I'm trying to solve for the distance...I tried doing this by first solving for the path difference by using L1-L2=(n+1/2)lambda, since we know n=2 and lambda=0.5. When I did this, I got the path difference as 1.25. I am now trying to solve for L2 (the distance from the speaker you...
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    Walking away from two loudspeakers-destructive interference

    I think I understand what you're saying...n should be 2, right?
  15. D

    Walking away from two loudspeakers-destructive interference

    I tried something but I'm not too sure whether it makes sense. using L1-L2=(n+1/2)lambda, I plugged in 1.41 for L1-L2 and solved for n since we know lambda is 0.5. By doing this I got n=2.32...would this confirm that the first value of n that you reach as you are walking away is 3?
  16. D

    Walking away from two loudspeakers-destructive interference

    So at the initial position, one speaker is 3.91 m away while the other is 2.5 m away, right? So the difference would be 3.91-2.5 which is 1.41. As you move, the path length difference decreases. The first value of n that you reach is 3, right?
  17. D

    Walking away from two loudspeakers-destructive interference

    Homework Statement You are standing 2.5 m directly in front of one of the two loudspeakers shown in the figure. They are 3.0 m apart and both are playing a 686 Hz tone in phase. As you begin to walk directly away from the speaker, at what distances from the speaker do you hear a minimum...
  18. D

    Finding the Time in a SHM Problem

    AHH woops...thanks so much for noticing that! :)
  19. D

    Finding the Time in a SHM Problem

    I have a feeling I only have to divide it by 2. Can someone verify this?
  20. D

    Finding the Time in a SHM Problem

    I divided it by 4 and got 0.67, which is incorrect...
  21. D

    Finding the Time in a SHM Problem

    I double checked my calculations and I'm getting that too. So now I just divide this value by 4?
  22. D

    Finding the Time in a SHM Problem

    Homework Statement Bungee Man is a superhero who does super deeds with the help of Super Bungee cords. The Super Bungee cords act like ideal springs no matter how much they are stretched. One day, Bungee Man stopped a school bus that had lost its brakes by hooking one end of a Super Bungee...
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    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    I got T=3, which is the correct answer. Thanks so much for all your help! :)
  24. D

    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    Yup, that makes sense...so E = U = 1/2kA^2, so at this point U is at its maximum value. As you said, for a simple harmonic oscillator, E is a constant...so this would mean that E is always equal to 1/2kA^2, right? E=1/2kA^2 U=1/8kA^2 T=? Is the above correct? Now I'm starting to understand...
  25. D

    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    I took a closer look at my notes. Is the total energy equal to the square of the amplitude?
  26. D

    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    Oh, I see what you're saying...but I'm a little lost at the conservation of energy part. I don't understand how to use that here. I know the potential energy is equal to 1/2k(A/2)^2 but isn't the kinetic energy just equal to 1/2mv^2? I understand that kinetic energy is related to the amplitude...
  27. D

    Ratio of Kinetic to Potential Energy of Simple Harmonic Oscillator

    Homework Statement Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude. Homework Equations KE=1/2mv2 = 1/2kA2sin2(wt) U=1/2kx2 = 1/2kA2cos2(wt) KEmax=1/2kA2 Umax=1/2KA2 The Attempt at a...
  28. D

    Kinematics - Projectile Motion

    Homework Statement You and your friend have been hired to see if the catapult a movie company owns will be usable for a scene about a battle set in the middle ages. In the scene a catapult launches a 750 kg boulder that is supposed to hit the ground 350 m away. The director is worried the...
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