# Search results

1. ### Wave mechanics?

The problem asks me to show that the addition of two cosines with different wavelength and frequencies gives a solution with beats. Mathematically, I need to verify that A cos (k1x-w1t)+A cos (k2x-w2t) is equivalent to A cos (.5(k1+k2)x-.5(w1+w2)t) cos (.5(k1-k2)x-.5(w1-w2)t) I converted...
2. ### Damped Oscillator probelm

Here's the problem: A damped oscillator has a mass of .05 kg, a spring constant of 5 N/m, and a damping constant of .4 Ns/m. At t=0, the mass is moving at 3.0 m/s at x=.1m. Find x as a function of time. What I have done: I know the damping constant b = .4 and I have used this to find...
3. ### Calculate the work done by a force

Yes...I have the forces for the dx direction to be zero. I'm still doing something wrong though?
4. ### Calculate the work done by a force

I get an answer of 2bL (1- x^2/a^2). This does not seem correct to me, since it contains an x^2 term? Is this right? Is there a substitution I can make for x? x=a or x=L, for instance? This problem is driving me crazy...any help greatly appreciated!
5. ### Calculate the work done by a force

So, for the first segment, dr = dyj. For the second segment, dr = dx i. For the third segment, dr = -dyj. For the fourth segment, dr = -dx i. Is this correct? Are the limits on my integration correct as well? Also, should the answer be 0 (closed path, conservative force...not sure if...
6. ### Calculate the work done by a force

I am asked to calculate the work done by a force as it moves around a path. The force is F = b(1-x^2/a^2)j. The path is a rectangle with coordinates at (0,0); (0,L); (a,L); (a,0). The force moves clockwise around the path beginning at the origin. A diagram is attached. I know work is...
7. ### Newton's Second Law

I think that velocity to be v0, not zero. Otherwise, the problem is trivial. I just wanted to check and make sure I wasn't missing anything :smile:
8. ### Newton's Second Law

It moves along the x-axis...I forgot to mention that. So gravity is not taken into consideration?
9. ### Newton's Second Law

Question answered! Thanks for the input!
10. ### Lagrange Problem redux - super

Thanks for being so prompt and helpful in your response! So, constrained to move in a circle...that sounds like polar coordinates! So the third term I am missing is the expression of kinetic energy for the disc in polar coordinates? So I should find the center of mass of the disk, and that...
11. ### Lagrange Problem redux - super

Thanks so much for the help...but I need some further clarification. You said that the contribution to KE comes from the fact that the disk's center of mass can move. How do I express this mathematically as a term in my kinetic energy expression? Is what I have for Kinetic energy thus far...
12. ### Lagrange Problem redux - super

Lagrange Problem redux -- super urgent... See the attachment to help you visualize this. A rod of length L and mass m is povoted at the origin and swings in the vertical plane. The other end of the rod is attached/pivoted to the center of a thin disk of mass m and radius r. OK, I know that...
13. ### LaGrange problem

We have a rod of length L and mass M pivoted at a point at the origin. This rod can swing in the vertical plane. The other end of the rod is pivoted to the center of a thin disk of mass M and radius R. Derive the equations of motion for the system. I have attached a drawing :) If you...
14. ### Lagrangian for system with springs

The system examined in the problem is depicted below: ^^^^^(m1)^^^^^(m2) m1 and m2 are connected by a spring and m1 is connected to the wall by a spring. The spring constant is k. T = m/2 [ x1'^2 +x2'^2 ] kinetic energy of system (x1' is velocity of m1, x2' is velocity of m2) U = 1/2 m...
15. ### Minimizing arc length

The problem I am working on asks me to find the curve on the surface z=x^(3/2) which minimizes arc length and connects the points (0,0,0) and (1,1,1). Here's what I did: Integral [sqrt(dx^2+dy^2+dz^2)] Integral [dx sqrt (1+(dy/dx)^2 +(dz/dx)^2] Integral [dx sqrt (1 + (dy/dx)^2 + 9x/4)]...
16. ### Lagrangian Dynamics problem - with setup

Lagrangian Dynamics problem -- need help with setup Here's the problem: A simple pendulum of length b and bob with mass m is attached to a massless support moving horizontally with constant acceleration a. Determine the equations of motion. For the pendulum, x = b sin theta and y = b cos...
17. ### Harmonic Motion Problem

Two masses connected by a single spring m1 --------m2 I hope this helps to make the geometry clear. I need help with this urgently :)

Please help with this! Harmonic Motion Two masses m1=100 g and m2=100 g slide freely in a horizontal frictionless track and are connected by a spring whose force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. I know omega = sqrt (k/m), but I have two masses...
19. ### Harmonic Motion Problem

Two masses m1=100g and m2=200g slide freely in a horizontal frictionless track and are connected by a spring whoser force constant is k=.5 N/m. Find the frequency of oscillatory motion for this system. Could someone give me a hint/help me get started on this? What equation(s) should I...
20. ### Evaluating indefinite integral - toughie!

Evaluating indefinite integral -- toughie! I have the velocity function v(x) = [(k*x^2)/(2*m)] + v0 I need to integrate this to get position as a function of time. So v = dx/dt. Separating variables, I get t = Integral [2m/(2mv0 + kx^2)] Here's where I'm stuck...If i pull out the 2m, then I...
21. ### Atwood's machine problem - inclined plane

Thanks for the input!
22. ### Need help - projectile motion with air resistance

Need urgent help -- projectile motion with air resistance Consider a projectile fired vertically in a constant gravitational field. For the same inital velocities, compare the times required for the projectile to reach its maximum height (a) for zero resisting force and (b) for a resisting...
23. ### Projectile Motion with air resistance - need help

Projectile Motion with air resistance -- need urgent help Consider a projectile fired vertically in a constant gravitational field. For the same inital velocities, compare the times required for the projectile to reach its maximum height (a) for zero resisting force and (b) for a resisting...
24. ### Projectile Motion - need help

Projectile Motion -- need urgent help :) If a projectile is fired from the origin of the coordinate system with an initial velocity v and in a direction making an angle alpha with the horizontal, calculate the time required for the projectile to cross a line passing thorugh the origin and...
25. ### Problem dealing with curl

Calculate the average value of the curl of the fluid for a rectangular path 15 cm by 10 cm, as shown in the figure (see file attachment). Va=(10i + 5j) Vb = (5i+10j) Vc= (5i + 10j) Vd = (10i + 5j) Could someone help me to get started with this one? Please :smile: Maybe give me an...
26. ### Question about Poisseuille's law and blood flow

I know that rate of flow is equal to pi*(P1-P2)*R^4/8nL. For blood in the coronary artery, I know the pressure drop, and the radius of the artery. What is the viscosity of blood? I can't find this value anywhere! And what value should I enter for L (distance L along a tube)? Is there an...
27. ### Expected Value Problem

Here goes: A potential customer for an 85000 dollar fire insurance policy possesses a home in an area that according to experience, may sustain a total loss in a given year with probability of .001 and a 50% loss with probability .01. Ignoring all other partial losses, what premium shoud the...

I understand 2a now! But could you elaborate a little more on the first problem? How do I start?

If someone could gtive me a general idea about how to approach these problems, I would be very grateful! Our class time was devoted to derivation rather than application. 1) Find the angle between the surfaces defined by r^2=9 and x+y+z^2=1 at the point (2,-2,1). 2) The height of a hill...
30. ### Quick dot product question

What is the dot product of a unit vector (e) with a non-unit vector (A)? Is this some sort of identity? Thanks, don_anon25

32. ### Coordinate Transformations

These problems are actually for my classical mechanics class, but they are linear-algebra based. I can construct a transformation matrix, but I have trouble visualizing the rotations, particularly in 3-space. So if someone could help me get a pictorial idea of what's actually happening, then...
33. ### Me again! (ideal gas/free expansion) soon

Here's my problem: An ideal gas is allowed to expand freely into an evacuated chamber. The gas is at a pressure of 5 bar and a temperature of 45 degrees Celsius. Find the final temperature and pressure of the gas. Find the entropy produced. W=0, Q=0, dU=0, and dT=0. So the final temp. is...
34. ### Free expansion of an ideal gas

Is there a different approach to this problem other than the one I've taken? I know: Q=0, W=0, dU=0, p1, and T1=T2. How do I get p2?
35. ### Free expansion of an ideal gas

The problem is that I only have the temperature and pressure of the entering gas, and no other data. Any ideas? Here's the actual problem: An ideal gas is allowed to expand freely into an evacuated chamber. The pressure of the entering gas is 5 bar and it has a temperature of 45 degrees...
36. ### Free expansion of an ideal gas

For the free expansion of an ideal gas into an evacuated chamber, I know that Work=0 and Q=0. Correct? This implies that the change in internal energy dU also equals 0. Since U depends solely on T, this should mean that the final temperature of the chamber is equal to the temperature of the...