(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle of mass m is in the xy plane so that it's position vector isr= acoswti+ bsinwtj, where a, b and w are positive constants a>b.

(a)Show that,

i) The particle moves in an ellipse

ii) the force acting on the particle is always directed towards the origin

(b) Find the,

i) Kinetic energy of the particle at A(a,0) and B(0,b)

ii) Potential energy at A and B

iii) The total energy of the particle and show that it is always constant.

2. Relevant equations

3. The attempt at a solution

(a)

i) I know this is the equation of an ellipse: (x - h)^{2}/ a^{2}+ (y - k)^{2}/ b^{2}= 1 but I find it hard to show the particle moves in an ellipse.

ii) I differentiated twice to geta= -w^{2}rso the minus sign shows that it is always directed to the origin.

iii) For a force to be conservative, the curl must be equal to zero. I tried doing that and got zero.

(b) I'm somehow stuck. I tried using 1/2mv^{2}but I don't know where to plug in the A and B.

iii) I know I should add the potential and kinetic energy to get the total energy and differentiate it to get something without t, but since I would not get the P.E and K.E, I couldn't go any further.

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# Homework Help: Motion in a plane

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