Particle \'a\' has a mass m, is initially located on thepositive x-axis at x = x
ID: 1763025 • Letter: P
Question
Particle 'a' has a mass m, is initially located on thepositive x-axis at x = x0 and is subject to a repulsiveforce Fx from particle b. The location of particle b isfixed at the origin. The force Fx is inverselyproportional to the square of the distance x between the particles.That is, Fx = A/x2 where A is a positiveconstant. Particle 'a' is released from rest and is allowed to moveunder the influence of the force. Find an expression for the workdone by the force on 'a' as a fuction of x. Find the kinetic energyand speed of 'a' as x approaches infinity. Particle 'a' has a mass m, is initially located on thepositive x-axis at x = x0 and is subject to a repulsiveforce Fx from particle b. The location of particle b isfixed at the origin. The force Fx is inverselyproportional to the square of the distance x between the particles.That is, Fx = A/x2 where A is a positiveconstant. Particle 'a' is released from rest and is allowed to moveunder the influence of the force. Find an expression for the workdone by the force on 'a' as a fuction of x. Find the kinetic energyand speed of 'a' as x approaches infinity.Explanation / Answer
1)we know small work done = F dx= A/x^2 dx if we integrate above equation we get Total work done=inegral (A/x2 ) dx (here minussign indicates for repulsive force) = -A/x+A/xo work done on a = A( -1/x+1/xo ) 2) kinetic energy=workdone because there is no potential energy as xtends to infinity 1/x tends to 0 kinetic energy at infinity = A/xo1/2 mv2 =A( -1/x+1/xo ) v={[(A( -1/x+1/xo )*2]/m} v at infinity =(2A/mxo)