The mechanical Equivalent of heat: total increase in temperature of the water?

[lalahelp]

Homework Statement

If in Joule's paddle wheel experiment a block of mass 10 kg is allowed to fall through 22.5 meters and the mass of the water is 50 grams. What is the total increase in temperature of the water?



Can your value of J be used for determining how much mechanical energy can be produced from a specified amount of thermal energy?

Homework Equations

Im not sure how to start the problems and do not know what to do could someone please help and explain them to me

 

[I like Serena]

What's the formula for potential energy (something with mass and height in it)?
And for thermal energy (something with mass and temperature in it)?

 

[lalahelp]

PE=mgh
Thermal energy= mct

what do I do from there?

 

[I like Serena]

Good!

PE=mgh

What would m be in this problem?
And g?
And h?

Thermal energy= mct

What would m be in this context?
Do you have a value for c?
How does t fit into your problem?

 

[lalahelp]

m=10 kg
g=9.8 m/s^2
h=22.5 m
___________
m=50 g
c=4185.8 kg c
t= I am not sure...

 

[I like Serena]

Right!

Now there is something called conservation of energy.
When your block falls, its potential energy has to go somewhere.
It is converted into heat.
What do you think the relation would be between the potential energy and the thermal energy?

As for "t".
What is it exactly that the problem asks you to calculate?

 

[lalahelp]

the potential energy equals the thermal energy?
the problem is asking for the total increase in temperature...

 

[I like Serena]

the potential energy equals the thermal energy?

Exactly!

the problem is asking for the total increase in temperature...

Yes. And "t" is the symbol for the change in temperature.

So...?

 

[lalahelp]

ohhh ok i got it Thank you!
could you explain the second question now lol your very helpful

 

[I like Serena]

What is J?
And what are your thoughts on it?

 

[lalahelp]

J is mgh/mct

My book does not say anything about it, it just gives an equation so I am not sure...

 

[I like Serena]

Okay, so you can calculate J, can't you?

Can you put into words what J signifies?

 

[lalahelp]

J means Joules... I thought it was only a unit...

 

[I like Serena]

Yes, J is usually the unit joule of energy.
That's why I asked, because the way J is used in your problem description suggests that J is used for something else...?
Where did your formula for J come from?

 

[lalahelp]

My physics book... its a conceputal problem. Yeh I was confused because it didnt say where that came from.

 

[I like Serena]

Conceptual problem or not, symbols always need to be defined before you can talk about concepts.
Is it defined as the formula you gave then?

 

[lalahelp]

My book says that's how you solve for J, so yes.

 

[I like Serena]

Can you put into words what the formula means then?

 

[lalahelp]

Yes it is defined as the formula

 

[I like Serena]

So what's in the nominator of the formula? And what's in the denominator?
Do you recognize those?