# A seemingly impossible problem

1. Mar 8, 2004

### blackflub

The water going over Niagara Falls drops 50.6 m. How much warmer is the water at the bottom of the falls thatn it is at the top? Disregard any possible effects of evaporation of water during the fall.

any help would be appreciated and the final answer is .118 C

2. Mar 8, 2004

### ShawnD

Energy is conserved:

$$\Delta$$thermal + $$\Delta$$potential = 0

$$mc \Delta T + mgh = 0$$

Factor out the m

$$(4187) \Delta T + (9.8)(-50.6) = 0$$

$$\Delta T = 0.1184$$

3. Mar 8, 2004

### blackflub

thanx soo much i guess i thought it was soo hard that i believed myself

4. Mar 8, 2004

### frznfire219

the unsettling thing is, what about the kinetic energy?

5. Mar 9, 2004

### HallsofIvy

What kinetic energy? The water as it falls, increases speed (so kinetic energy also) as it loses potential energy. However, when it hits the bottom, it stops going down! There will be some small motion of water but it will be so turbulent that eventually it will be converted to heat. In the long run all the energy is converted to heat.

6. Jan 26, 2012

### joehoy41

where did u get 4187?

7. Jan 26, 2012

### Curious3141

The c term, the specific heat capacity of water in J/(kg.K).

BTW, this thread is nearly 8 years old!