A particle slides down a frictionless parabolic track starting from rest at point A. Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then a) KE at P = KE at B b) height at P = height at A c) total energy at P = total energy at A d) time of travel from A to B = time of travel from B to P
A particle slides down a frictionless parabolic track starting from rest at point A. Point B is at the vertex of parabola and point C is at a height less than that of point A. After C, the particle moves freely in air as a projectile. If the particle reaches highest point at P, then a) KE at P = KE at B b) height at P = height at A c) total energy at P = total energy at A d) time of travel from A to B = time of travel from B to P

 

Answer: The correct answer is c) total energy at P = total energy at A

Because energy is always conserved (unless in inelastic collisions), the total energy at A and P will always be equal. However, Kinetic Energy varies depending on the particle’s velocity. At Point P, the object’s velocity is zero (Highest point), but not at B. The object at the highest point has no kinetic energy and just potential energy, therefore its height at P will be less than its height at A. A has kinetic and potential energy at point A. (Energy conservation law) The time taken from A to B will be longer than from B to P due to the greater distance. ( Height A is greater than P)