What is the relationship between height and velocity for a falling object?

[maxximo1]

First of all, I have to say hello to all of you. I am from a foreign country so my English isn't so good. So my problem will probably seem very funny and easy to you, but it's very hard to me. I've got absolutely no idea about it and I'd be very thankful if you could help me out.
So here it is.

I need to find out the height, from which a piece of lead was dropped down to Earth and it's temperature grew up by 10 Celcius degrees (50 Fahrenheit degrees). We assume that only the internal energy of the piece of lead grew up and that internal energy of Earth didn't.

Cheers.

 

[HallsofIvy]

I'm not sure I understand the problem. WHY would the termperature of the lead increase? Are you saying that when the piece of lead hit the ground all of the original potential energy (which was kinetic energy just before it hit) went into the internal energy of the lead? It that's the case you need to determine how much energy was required to raise the temperature by 10 degrees Celcius. The specific heat of lead is, I believe, 0.13 Joules per gtam per degree Kelvin (one degree Kelvin is the same size as one degree Celcius). You don't give a mass for the piece of lead but that should cancel out in setting internal energy equal to potential energy anyway.

 

[maxximo1]

You see, the specific heat of lead is 129 J/kg*K, so if the mass of the piece of lead would be 1 kg, I would need 1290 Joules to make the lead raise its temperature by 10 degrees Kelvin. But the main problem is that I DON'T know the mass and I need to get the height of dropping the piece, not the energy needed to raise its temperature. Please help me : (

 

[Zach Smith]

I think I can help here: When the object hits the floor, its energy is changing from kinetic to thermal. Either way, it has the same net energy due to conservation of energy.
So we know that the kinetic energy lost is equal to the thermal energy gained.

What is the expression for the amount of kinetic energy lost?
What is the expression for the amount of thermal energy gained?

These two will be balanced with each other, so you can find the velocity of the object the moment before it hits the floor, and from this the distance it has traveled (since you know the acceleration acting upon it).