Question

which has a greater velocity at the equilibrium position? a) A 1kg mass attached to as spring of K=100N/m in horizontal frictionless surface after releasing it from a compression of 10cm. b) A 1kg mass oscillating on a concave-upward smooth surface with an effective vertical length of 5cm. c) A pendulum bob of mass 1kg displaced through a vertical height of 10cm. d) All of these could not be compared.

Answer 1

this is a question of conservation of energy.

since potential energy = kinetic energy

hence the system having highest potential energy will be having maximum kinetic energy and since kinetic energy is directly proportional to velocity hence the more will be velocity

case 1

potential energy in spring is given by

where x is the compression = 10 cm = 0.1m and k = 100 N/m

therefore P = 0.5 x 100 x 0.01 = 0.5 J

case 2

since potential energy is give by P = mgh where h is height = 5 cm =0.05m, g = 10 m/s^2 and m = 1 kg

hence P = 1 x 10 x 0.05 = 0.5J

case 3

since potential energy is given by P = mgh where h = 10 cm = 0.1m

hence P = 1 x 10 x 0.1 = 1 J

hence case 3 i.e. pendulum has maximum potential energy hence thus at equilibrium it will have maximum velocity as all three masses are same