# Homework Help: Kinetic energy to heat problem

1. Apr 25, 2013

### ryu1

1. The problem statement, all variables and given/known data
1.5ton (1500kg) object is dropped from 20 meters into a bucket with 2.5L of water in it.
All the kinetic energy is transferred to the water in form of heat.
What is the temperature rise of the water?

2. how much the water temperature rises if the object lifts during it's fall, another mass(no friction involved) making it do work, spending 900.0 J before hitting the water.

3. The attempt at a solution
right not sure if i did this right but i might did:
Ek = 0.5*1500kg*(9.81ms^-2)^2 = 750kg*96.2361m/s = 72127.075m/s
72127.075m/s = 72.127KJ
specific heat of water = 4.19KJ/Kg*C
so
72.127KJ = 4.19KJ/Kg*C * 2.5Kg[=2.5L of water right?] *dT
dT=6.886C

temperature rise by 6.886 degrees Celsius.
is that actually correct?

right, for the 2nd problem, can we just decrease 900 from the 72127.075m/s (=72127.075J) and then calculate the whole thing exactly the same way?
arriving to dT=6.7997 Celsius?

please let me know if I am correct on this.
Thanks a lot! :)

Last edited: Apr 25, 2013
2. Apr 25, 2013

### Dick

Try the first one again. If a is the acceleration then kinetic energy is NOT equal to (1/2)ma^2. Find a different formula.

3. Apr 25, 2013

### ryu1

is it Ep = 1500KG*9.81m/s^2 *20m ? then i get 294.3KJ

Is that correct? but this one is Potential energy so I got confused when talked about kinetic in the question.

4. Apr 25, 2013

### Dick

Yes, that's the one. If the mass get stopped by hitting the water then all of the potential energy will get tranferred to kinetic energy and transferred to the water. (1/2)ma^2 isn't a kinetic energy. It's not much of anything relating to energy. The units are all wrong.

Last edited: Apr 25, 2013
5. Apr 25, 2013

### ryu1

so I go exactly the same way from this point?
294.3KJ/10.475KJ*C = 28.095C =dT

?

it does seems to be more realistic i guess.
and the 2nd problem would be
294300-900=293.4KJ
dT = 293.4/10.475 = 28.009C
?
That is really close , but it's plausible if the change is only 900J ...is that right?
thats the last question in my homework, I have been sitting on the last 3 questions all night through (it's 7am now)
Thanks!

6. Apr 25, 2013

### Dick

Sounds ok. I didn't check the exact numbers. But you dropped an awfully heavy thing a pretty large distance into a small amount of water, hence the large temperature change. For the second part you really didn't change the energy much, so the temp change should be only a little less.

7. Apr 26, 2013

Thank you.