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...
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?
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...
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.
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...
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.
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...
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...
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?
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?
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...
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...
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...
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...
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...
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...