# Search results

1. ### Need help understanding problem about Young's double slit

"In Young's double slit experiment, assuming the distance between the slits is 0.07mm and the wavelength of light used is 600 nm, when the screen is 70 cm away, what kind of interference is there." I'm not sure what I'm being asked to determine here. Plugging in the figures into the...
2. ### Need hint on 'simple' differentiation problem

I need to differentiate z = artan(y/x) with respect to x. Somehow z' = y/(1 +(1/x)^2) doesn't seem right.
3. ### Cauchy integral problem: can this answer be simplified further?

The question calls for using Cauchy's integral formula to compute the integral for Int.c z/[(z-1)(z-3i)] dz, assuming C is the loop |z-1|=3. Taking z = 1 and f(z) = z/(z-3i), I came up with (2pi*i)/(1-3i), which seems like it could be simplified, but I'm not sure how.
4. ### Partial fraction of integrand

I need to find the partial fraction expansion of the integrand z/[(z-2i)(z+i)] Just doing 1/(z-2i) + 1/(z+i) results in (2z-i)/(z-2i)(z+i). It seems easy, but I can't figure out what to multiply by to get the correct numerator.
5. ### Partial fraction of integrand

As part of finding the integral of z/(z^2 -1), I'm stuck on getting the partial fraction for it. 1/2 [(1/(z-1) - 1/(z+1)] gives 1/(z^2-1). What should I do to get the z in the numerator. Any hints welcome. Regards
6. ### Complex analysis question

Cauchy integral question The question calls for finding the integral of dz/((z-i)(z+1)) (C:|z-i|=1) I can't figure out how to do this for (C:|z-i|=1). How does this differ from, say, (C: |z|=2) Regards
7. ### Explanation of path integrals

What exactly does a path integral measure? Is it area between the ends/bounds of the line? Or is it the length of the line? Just started complex analysis and am comletely confused by this.
8. ### Time difference between two sine waves

"There are two sine waves having a phase difference of 20 degrees. After one reaches its maximum value, how much time will pass until the other reaches its maximum, assuming a frequency of 60 Hz." Should I go about this by assuming... sin(120pi*t) = sin(120pi(t + x) - 20) Any hints...
9. ### Integral problem: need help landing this

The problem is to find the definite integral of e^2x/(e^x + e^-x) with the limits of 0 and log 2. Finding the integral was easy enough, e^x - log (1 + e^2x) , but how do I plug log 2 into this. Any hints appreciated.
10. ### Integral of 1/(1 + cosx)^2

Just finished working out the integral of 1/(1 + cosx)^2 as (1/2)(tan(x/2)) + (1/6)(tan (x/2))^3 + C I'm just wondering whether it's possible to use any substitutions to simplify this further. regards
11. ### Integral of cos^3 theta

Would very much appreciate a hint on how to start this off. So far I have cos theta = (1-t^2)/(1+t^2). After squaring this and doing various substitutions, I get (cos theta)^3, which can't be right.
12. ### Stumped again: Water flow speed Q

I've struggled with this since this morning with hardly any progress. "There is a level pipe filled with water flowing through it. Branching off from this pipe are two pipes going perpendicularly upward, with a cross sectional area Sa, Sb, respectively, and there being a difference in water...
13. ### Young's modulus problem - need a hint

Young's modulus problem -- need a hint There are two wires, one brass the other copper, both 50 cm long and 1.0 mm diameter. They are somehow connected to form a 1m length. A force is applied to both ends, resulting in a total length change of 0.5 mm. Given the respective young's moduluses of...
14. ### Simple oscillation problem - help needed

"An object is moving along the x-axis in simple harmonic motion. It starts from its equilibrium position which is at the origin at t=0 and is moving to the right. The amplitude of its motion is 2 m and its frequency is 3 hz. (1) Determine the expression for the objects displacement. (2) Where is...
15. ### Brain cramp on 2nd elevator problem

"An elevator is moving upward at a constant velocity of 2.5 m/s. A ball is launched straight upward from the floor of the elevator with an initial velocity of 4.9 m/s (relative to the floor). (1) Determine the time the ball takes to reach its highest point from the standpoint of a person not...
16. ### Elevator acceration problem

"In an elevator that is moving with constant acceleration, a person of 50 kg mass is standing on a bathroom scale that shows "55 kg". Determine the accerlation of the elevator." I'm pretty sure my answer is right. I'm just wondering if there's another way. So, 55 kg is 1.1 times 50 kg...
17. ### Ball, spring and curved incline - is this right?

Ball, spring and curved incline -- is this right? Picture a smooth, level, frictionless surface (A) that leads into a curved incline (B-C). The top of the incline (C) is 0.4 meter above the flat surface. At the start of A is a spring with a spring coefficient of 10, with one end fixed and a...
18. ### Stuck on conservation of energy problem

"On a frictionless, horizontal surface there is a spring with one end fixed and the other attached to a board of mass 1 kg. The spring coefficient is 150 N/m. 500g of clay moving at 3.0 m/s on this horizontal surface collides squarely with the board. As a result, the board and clay stick...
19. ### Person-jumping-out-of-a-moving-boat problem

I'd appreciate a hint on how to start this one. "A person weighing 50kg is riding in a 400kg boat heading due east at 3.0 m/s. The person jumps horizontally out of the boat in the other direction (i.e., westward). Just after he jumps, the velocity of the boat as seen from the person is 4.5...
20. ### Baseball-bat impulse question

A 0.15 kg ball traveling horizontally at 6.0 m/s is hit by a bat, after which it is traveling at 8.0 m/s perpendicular to the original direction. I'm supposed to determine the impulse that the ball receives from the bat. Since cos90 is zero, would this just be the mass multiplied by the...
21. ### Stuck on sliding object problem

I'd appreciate a tip here. A 10 kg object on a horizontal, unsmooth table is pushed to the right so as to have an intial velocity of 20 m/s. It comes to rest 5 seconds later, during which time its acceleration (deceleration?) was constant. I've already figured out the acceleration (4 m/s^2)...
22. ### Weight on a string question

A weight weighing 0.2 kg is attached to a string that is raised/lowered vertically by hand. When the pulling force is 2.5 N, I'm supposed to find the acceleration. Since the normal force in this case is N=mg=0.2(9.8)= 1.96 N, would the acceleration simply be the net force (2.5 N - 1.96 N =...
23. ### Before I attempt this next problem on sliding blocks

I'd like to make sure I understand it. It reads... "Two objects, A and B, are placed in contact with each other on a horizontal, frictionless surface. Object A weighs 1.5kg, and B weighs 2.5kg. If a force of 8.0N is exerted on the surface of object A in contact with B AND on the opposite...
24. ### Weights on a string problem - is this right?

Weights on a string problem -- is this right?? Hello all, I'd appreciate it if anyone can check whether I have the right approach to this problem: "Two weights, A and B, are connected by a string. Weight A weighs 0.7 kg, and B weights 0.8 kg. If A is raised vertically upward with a force...
25. ### Need help with projectile motion problem

Hi there, I'd really, REALLY appreciate a hint for solving the following projectile motion problem. "A ball is thrown upward at an angle from a point on a horizontal plane. 10 meters away from that point is a wall. The ball strikes the wall perpendicularly at a height of 4.9 meters. (1)...