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  1. R

    Constraint relations

    Referring to the diagram: The Perpendicular distance from the pulley to the axis of the ring is say a constant L. The part of the string that is being pulled (variable) is say y. The movement of the ring on the X-axis is also changing (variable) and we take it as x. Now, using the...
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    What is the formula of ellipse in 3D space

    what about (x^2/a^2) + (y^2/b^2) + (z^2/c^2)=1 ? (intuitive) However, the equation of a circle in 3D is always defined by the equation of a sphere and the plane which cuts it. The sliced portion is the required circle. So it may be a similar case with the ellipse. Something like one half of a...
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    C/++/# Spiralling Algorithm in C++

    This one is a little tricky because the numbering starts from the center. I have already figured out how to do this when the numbering starts from the top left hand corner (recursion) using "virtual motion analogy" (that's what I like to call it).However,looping with for or while is clumsy...
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    C/++/# Spiralling Algorithm in C++

    Hey, I got an assignment to write and algorithm in C++ to print this pattern: 35 34 33 32 31 30 16 15 14 13 12 29 17 04 03 02 11 28 18 05 00 01 10 27 19 06 07 08 09 26 20 21 22 23 24 25 As you...
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    Projectile Motion of shot cannon ball

    Yeh, the question is not very clear...when a golf ball is hit, its distance is naturally going to increase from the origin, then where does the maximum angle come in?
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    Tangent and normal acceleration, curvature radius

    What exactly are the tangent and the normal accelerations of a projectile motion and how are they expressed mathematically? What is curvature radius? What is its expression? How is it derived ?
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    Doppler effect bat

    At first the frequency received by the prey is: \nu' = \nu (\frac{v-v_{L}}{v-v_{S}}) Now, as you said correctly, the wave is reflected back and the the source and listener interchange to give us this i.e. the bat becomes the listener and the prey the source of the reflected sound wave...
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    Physics: doppler effect (observer & source in motion)

    Is this what you get on simplifying the above equation? f'=f(\frac{v+v_{obs}}{v-v_{s}} ) Try not to apply the equation directly. Since, the frequency is received by the car at that moment t_{0} surely the sound wave of that frequency which we have to find out must have left some time...
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    Exercising Loop: Pattern

    The first one is quite simple: Given the size of the array as 5, You have to put the "x" in the boundary of the square and on the right diagonal. condition for printing right diagonal: if(r==c){print "x"} condition for printing boundary: if(r-1==-1||r==n-1||c==0||c-1==-1){print "x"}...
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    Dopplers Effect Problem

    Frequency of reflected wave: \nu'=\nu (\frac{v+v_{L}}{v}) Now, the source and listener interchange as the sound wave is reflected:(as received back by operator) \nu''=\nu'(\frac{v}{v-v_{L}}) \nu''=410 Hz \nu=400 Hz Plugging in the values we get 3m/s solving for...
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    Dopplers Effect Problem

    Homework Statement 1. A car moves with a speed of 54km/h towards a cliff.The horn of the car emits a frequency of 400Hz at a speed of 335m/s (a)Find the wavelength of the sound emitted by the horn in front of the car (b)Find the wavelength of the wave reflected from the cliff (c)What...
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    Combination problem

    Homework Statement A closet has 5 pairs of shoes. The number of ways in which 4 shoes can be chosen from it so that there will be no complete pair are? Homework Equations Permutation and Combination formulae The Attempt at a Solution I tried but couldn't figure it out anyway.
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    Equilibrium of Cylinder with two liquids at either side

    Homework Statement (Please refer to the attachment given) In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2\rho and 3\rho . The height h for the equilibrium of cylinder must be: a) \frac{3R}{2} b) R...
  14. R

    Atwood Machine Problem

    Thank you very much for your help and support!
  15. R

    Atwood Machine Problem

    Is this correct?
  16. R

    Atwood Machine Problem

    Lets see...F2=mg, F_{2}+mg-T=ma ...(1) T-mg=ma ...(2) Adding both sides, we get mg+mg-mg+T-T=2ma mg=2ma a=\frac{g}{2} then a_{3}=\frac{g}{2} Therefore, the correct option would be no. (b) a1>a3>a2
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    Atwood Machine Problem

    For the second pulley we can straight forward apply the equation and with that we get the acceleration a2 = g/3 Yes, you were right. The acceleration have to be calculated individually. For the first pulley let the tension in the string be T1 which will be equal to the force pulling F1=2mg...
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    Atwood Machine Problem

    Homework Statement In the three figures given in the attachment consisting of three atwood machines with, the blocks A, B and C of mass m have accelerations a1, a2 and a3 respectively.F1 and F2 are external forces of magnitude 2mg and mg acting on the first and third diagrams...
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    Indefinite Integration Problem

    Is this right? the square root of the sum of the squares of the coefficients of the sine and cosine is \sqrt2. Therefore, we multiply both the numerator and the denominator by \frac{1}{\sqrt2}: \frac{1}{\sqrt2} \int \frac{1}{\frac{1}{\sqrt2}\sin{x}+\frac{1}{\sqrt2}\cos{x}} dx...
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    Indefinite Integration Problem

    This is an interesting proposition, however, I have not come across the given identity yet or the anti-derivative of sec(x). So either I do it in a different way or learn these new identities, the proof of which I would be glad if you could post a link to. By splitting, is this what you mean...
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    Indefinite Integration Problem

    Homework Statement Integrate: \int \frac{1}{\sin{x}+cos{x}}dx Homework Equations The one above and basic integration formulae which need not be mentioned. The Attempt at a Solution \int \frac{1}{(\sin{x}+cos{x})}...
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    Trigo Prob to prove

    Looks like I got it; beginning from where I left, 1-\sin{2\alpha} = \cos^2{\alpha-a\cos^2{\alpha}+\sin^2{\alpha}+a\sin^2{\alpha}-(\sin{2\alpha})(\sqrt{1-a^2}) -After taking 'a' common... Since, \cos^2{\alpha}+\sin^2{\alpha}=1...
  23. R

    Trigo Prob to prove

    No, it is a scalar multiplying the last sine term.
  24. R

    Trigo Prob to prove

    Homework Statement if: (1+\sqrt{1+a})\tan{\alpha} = (1+\sqrt{1-a}) Prove that: \sin{4 \alpha} = a Homework Equations \cos{2\alpha} = 1-2\sin^2{\alpha} \tan{\alpha} = \sqrt{\frac{1-\cos{2\alpha}}{1+\cos{2\alpha}}} The Attempt at a...
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    Acceleration From Earth's Rotation

    Tangential acceleration is acceleration along the surface of the Earth (if there is) such that from that point you tend to go in a straight line forming a right angle with the line joining you and the centre of the Earth.The Earth has a constant angular velocity and not acceleration.Yes, the...
  26. R

    When Is Violence Justified?

    There are three answers (solutions) to this problem.It is justified relative to the person who has been hurt by the initial violent act, but it is not justified to the person who initially caused the violence as that person would in no way would want to receive back violence. In a concious frame...
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    Good and Bad Explained!

    All ambiguity would end if 'consciousness' would be understood.
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    When Is Violence Justified?

    The question is not about violence, but about the meaning of justification
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    Good and Bad Explained!

    At this critical juncture, let me bring another concept which defines the 'attribute' of being good and bad. I had a problem.It had been bothering me for a while and as far as I could see it had the least of all wishes to leave me.It was causing immense suffering to me;a lot of pain, struggle...
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    Fermat's Last theorem

    yes,its like a stack of books.If the the lower books hold, then the upper books will also hold .Already established axioms are like the lower books and the newer proofs depend on them.
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