Starting from rest a 00367kilogram steel ball sinks into a v

Starting from rest, a 0.0367-kilogram steel ball sinks into a vat of corn syrup. The thick syrup exerts a viscous drag force that is proportional to the ball\'s velocity: where C = 0.270 N- s/m is a constant related to the size and composition of the ball as well as the viscosity of the syrup. Find the rate at which gravitational energy is converted to thermal energy once the ball reaches terminal velocity. After the ball reaches terminal velocity its kinetic energy is constant Any further work done by gravity is therefore directly transferred to the syrup and ball as thermal energy The rate at which the energy is converted is the power supplied by gravity: where F is the force, v is the speed of the ball and B is the relative angle between the force and velocity vectors. The terminal velocity of the ball can be determined from the given information using Newton\'s Laws.

Solution

At Terminal Velocity Weight is balance by drag force

mg =Cv

=>v=mg/C =0.0367*9.8/0.27

v=1.332 m/s

The Rate at which gravitational energy is converted to thermal energy is

P=Fv =(0.0367*9.8)*1.332

P=0.48 W