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  1. M

    Roller Coaster total distance

    No, we haven't reached integration yet so he is not expecting us to solve it by integration. We're just about to finish differentiation. Thank you so much for the help. I appreciate it. It was supposed to be challenging he said, so I was thinking it's not going to be that simple. But how...
  2. M

    Roller Coaster total distance

    A ride on each of 3 different roller coasters lasts exactly 60 seconds. The horizontal position of each of the roller coasters (in meters) as a function of time (in seconds) is given by Streaker: S(t) = 4sin(t)cos(t) Redhawk: S(t) = et/(t2-400) Dragster: S(t) = (3600 - t2)3/2 Find...
  3. M

    Roller Coaster total distance

    Because I'm trying to compare 3 different roller coasters to see which one covers the most distance, the greatest velocity and the biggest acceleration during the 60 second ride. The equation S(t) = 4sin(t)cos(t) is the POSITION of the roller coaster with respect to time for one of the roller...
  4. M

    Roller Coaster total distance

    Well I was confused because I thought S(60) -S(0) is displacement instead of total distance traveled?? I used S(60) -S(0) and got 1.16(thinking that is the displacement). Divided that by time( = 60s) and got average velocity of .019m/s.
  5. M

    Roller Coaster total distance

    Homework Statement A roller coaster ride lasts only 60 seconds. What is the total distance traveled during the 60 seconds, given the position of the roller as a function of time is s(t) = 4cos(t)sin(t). Homework Equations Position as a function of time S(t) = 4cos(t)sin(t) The...
  6. M

    LC Circuit with DC power supply

    Ok that was very helpful, thanks. I guess the graph i drew for q vs t is wrong since charge is not oscilatting around zero; but I can fix that. So about energy transformation: *Before the switch is closed, at t < 0, the capacitor is fully charged and it has all the energy(in it's electrical...
  7. M

    LC Circuit with DC power supply

    Could you please briefly explain your first sentence again? I don't think I get it that well. But this is what I did: w = sqrt(1/LC); Period = 2*pi/w; Total energy = (q02)/2C + .5*L*I2; phi = cos-1(q0/qmax). Now I want to find the maximum power storage in the battery during the circuit...
  8. M

    LC Circuit with DC power supply

    A circuit has a battery(V), Capacitor(C) and Inductor(L) connected in series. At t < 0, the switch is open and the capacitor has an initial charge of -800uC and Io = 0.0Amps.. When the switch is closed at t = 0, I want to know what happens here. I only understand an LC circuit where there is...
  9. M

    RL Circuit

    I am trying to analyse an RL circuit, particulartly the dependence of current in 2 resistors with time, in an RL circuit. This is what I think but I would really love some people to tell me if I am getting it wrong or if there is anything they want to add to it. ***Just after the the switched...
  10. M

    Linearly dependent sets

    Thanks rasmhop... I did think "A" being an invertible matrix could make a difference but I didn't know how to prove it. That was a very good help from you.
  11. M

    Linearly dependent sets

    That makes sense. So if we have a1(Av1) + a2(Av2) + a3(Av3) = 0, then at least one of the constants could be zero and that will definitely result to a linearly dependent set. Thanks. That leads me to a related theory: Let's assume we are talking about {v1, v2, v3} being a linearly...
  12. M

    Linearly dependent sets

    If A is a 3x3 Matrix and {v1, v2, v3} is a linearly dependent set of vectors in R^3, then {Av1, Av2, Av3} is also a linearly dependent set??? Is this true? Can someone please explain why or why not?? What I think: I think it is true because I read that a linear transformation preserves the...
  13. M

    Conservation of linear or angular momentum + center of mass.

    Well maybe I should design a question to explain what my statement means. Let's say a projectile(mass Mp, initial velocity Vpi, final velocity Vpf) collides with a thin rod(mass Mr, length L, initial velocity is zero, Inertial mass I, angular speed W). The rod is pinned at it's center on a...
  14. M

    Conservation of linear or angular momentum + center of mass.

    So I did more reading and this is what I am understanding: In a closed system(system upon which no external forces act), both linear and angular momentum are conserved. So if we say this is a collision between a "resting thin rod(pinned at it's center)" and a "small object" on a frictionless...
  15. M

    Conservation of linear or angular momentum + center of mass.

    What do you mean by total linear and angular momentum? Would that be like momentum "before" and "after" say in a collision? So if we consider this as a collision between a small object and the resting rod(pinned at center). I will say total linear momentum of the collision is NOT conserved...
  16. M

    Conservation of linear or angular momentum + center of mass.

    So I have been reading about conservation of linear momentum and conservation of angular momentum of a rotating object. For example a thin rod resting horizontally on the a flat surface. If this rod is being hit by a small object(collision), the rod will rotate about it's center of mass and will...
  17. M

    Work energy theorem vs Newton's 2nd law and kinematics

    Ok, so I'll say Work Energy Theorem(W.E.Th) might be easier if - *We do NOT have to deal with time. *We know info(velocity and energy) about the starting and ending point of the object's motion. *I also thought W.E.Th will be easier since it only involves scalar multiplication. Scalars are...
  18. M

    Work energy theorem vs Newton's 2nd law and kinematics

    So i have this general question. When the situation arises in which there are velocity and/or position depended forces acting on an object, would it be generally easier to use the work energy theorem or Newton's 2nd law & kinematics in predicting the motion? My guts tell me it will be work...
  19. M

    Static & kinetic friction could cause motion?

    Static & kinetic friction could cause motion?? Homework Statement I have a question about friction. I was asked to discuss an example where static friction and kinetic friction could cause motion. One example for each. I have never learnt friction causing motion and I thought of it but...
  20. M

    Maximum photocurrent ejected by electrons in photoelectric effect

    I have found the magic formula from someone. It's power divided by the Energy of the photon, and then multiplying that answer by e(charge of an electron). I ended up getting 9.1mA.
  21. M

    Maximum photocurrent ejected by electrons in photoelectric effect

    Does anyone know how to determine the maximum photocurrent that could be produced by ejected electrons in a photoelectric effect experiment_(as unpolarized beam of light incidents on a metal surface)? I don't know of any formula that calculates the photocurrent and I could not derive any. I...
  22. M

    Time and amplitude in a standing wave.

    1. A string vibrates in its 3rd harmonic standing wave pattern. The mass and length of the string are given. Also given is the tension in the string and the transverse velocity of the string at the antinode located at x = Length/2 when the standing wave has no displacement at t = 0.00s M =...
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