Question

Starting from rest, a 0.0367 kg 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. → F drag = − C → v 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.

Answer 1

0.48 W

Step-by-step explanation:

Given that:

the mass of the steel ball = 0.0367 kg

C = 0.270 N

g (acceleration due to gravity) = 9.8

Now;

At Terminal Velocity Weight is balance by drag force

mg =Cv

Making v the subject of the formula:we have:

`v = \frac {mg}{C}`

`v = \frac {0.0367*9.8}{0.270}`

v = 1.332 m/s

Thus, the Rate at which gravitational energy is converted to thermal energy once the ball reaches terminal velocity is:

P=Fv

P = mgv

`P = (0.0367*9.8)*1.332`

P=0.48 W