Answer to Question #271389 in Physics for Princeoffiong

Question

1) Find an expression for the velocity of water just before it hits the floor of a water fall if the temperature change is tita when it hits the floor

2) what is the time of heating water of 30kg using an electronic coil with 240V accross it, with a current of 13A flowing through it. Given that the specific heat capacity of water is 4200j/kg

Answer 1

1) Assuming the water started falling from rest and the entire kinetic energy converted into heat:

$$\frac12mv^2=cm\theta,\\ v=\sqrt{2c\theta.}$$

2) Find the power of the heater:

$$P=IV.$$

The electrical energy is power times time:

$$E=Pt=IVt,$$

on the other hand,

$$E=cm\Delta T,\\\space\\ IVt=cm\Delta T,\\\space\\ t=\frac{cm\Delta T}{IV}=4038\text{ s, or 67 min 18 s}.$$

We assumed the water must be heated from 0 to 100°C.