# How fast must you throw a snowball against a wall in order to make it melt?

1. Oct 31, 2006

### twotaileddemon

Hi, I'm new to this forum and I have a question.

In my physics class we are discussing energy and work. We are given this problem:

"It is exactly 0*C. How fast must you throw a snowball against a wall in order to make it completely melt? (Assume all the energy is transferred to the snowball and neglect air friction)"

Now.. considering there is almost no information given, how am I supposed to solve this? I know potential energy is mgh and kinetc is .5mv^2. Work is Fs, or change in kinetic energy. It's just.. give so little details I don't know where to start. Can anyone tell me how to start the problem, or any general guidance without giving the answer? Thanks :)

2. Oct 31, 2006

### marcusl

How much energy do you need to turn ice into water?

3. Oct 31, 2006

### twotaileddemon

I'm not really sure.. we never went over that. Is it just an equation that I'm looking for?

4. Oct 31, 2006

### twotaileddemon

I'm pretty sure kinetic energy is used somehow. And this may be completely off, but could you do something with specific heat or melting/boiling points? I'm given no numerical values to work with.. so I'm a bit lost xx;;

5. Oct 31, 2006

### Max Eilerson

6. Oct 31, 2006

### twotaileddemon

.5m(Vf-Vo)^2 = Ei+El i = initial l = lost
Is this okay?

7. Oct 31, 2006

### Max Eilerson

Yes that's fine. Although I'm not sure what you mean by energy lost, the energy is gained by the snowball and then converted.

Last edited: Oct 31, 2006
8. Oct 31, 2006

### twotaileddemon

So to solve for Vf, I would get
sq rt (Ei + El + .5mVo^2)/(.5m) = Vf

9. Oct 31, 2006

### marcusl

You need to find the energy needed to melt the snowball. Use the mass and heat of fusion.

10. Oct 31, 2006

### Max Eilerson

$$Ei = 0.5mV_{i}^2 = 0$$
$$mL = 1/2mV_{f}^2$$, L = latent heat of fusion
$$=> V_{f} = sqrt(2L)$$

You can think of m being 1 gram, basically your using a unit mass for L.

edit: put 0 instead of f sorry.

Last edited: Oct 31, 2006
11. Oct 31, 2006

### twotaileddemon

I guess I'm so confused is because I've never heard the term latent heat of fusion until now, and it was not discussed in class. So sorry if I seem clueless.. because I am xx;;

So the sq rt of mVo^2 would be the correct answer when substituting 1/2mVo^2 for L, ... the 2's cancel out and you're left with sq rt mVo^2? Or do you add the .5mVi^2 to it?

12. Oct 31, 2006

### twotaileddemon

Uh.. oh I see. Vf was already derived. So sqrt of 2L is the answer? There is no other way to simplify it, because my teacher is going to wonder how I came up with that when we didn't discuss it xx;;

I'm so sorry for wasting everyone's time too. I appreciate all the help immensely.

13. Oct 31, 2006

### twotaileddemon

Okay so let me just get something straight. L = 1/2mVf^2
Vf = sqrt 2L

Where does the mass of the snowball go in the equation?
Vf = sqrt 2(1/2mVo^2) = sqrt mVo^2
?

14. Oct 31, 2006

### Max Eilerson

15. Oct 31, 2006

### marcusl

Max Eilerson, why did you choose Ei=0? Snowball has non-zero kinetic energy before collision, zero final kinetic energy.

KEi=(m*v_i^2)/2
This must equal the latent heat of fusion of snowball, which is
L=m*334 kJ/kg

equate these and solve for v_i.
Does that make sense twotaileddemon?
Do you need to know the mass?

Edit: I had typo in specific latent heat value 334

16. Oct 31, 2006

### twotaileddemon

I did read the page, thanks for it.
So Vf is sqrt of 669 J which is about 25.86 J... okay. Thanks :). I will ask my teacher tomorrow whether or not this is allowed since we haven't learned it yet.. maybe he wanted us to do research. Thanks again, I really really appreciate it :)

17. Oct 31, 2006

### Max Eilerson

marcus I got my subscripts confused sorry.

The kinetic energy doesn't equal the latent heat of fusion of the snowball it equals mL.

18. Oct 31, 2006

### twotaileddemon

Max Eilerson, why did you choose Ei=0? Snowball has non-zero kinetic energy before collision, zero final kinetic energy.

KEi=(m*v_i^2)/2
This must equal the latent heat of fusion of snowball, which is
L=m*334 kJ/kg [So do you isolate v_i.. so I get sq rt 334 J / 2kg as my answer? or simplifying it, 117 J / kg? = 117 m/s?

equate these and solve for v_i.
Does that make sense twotaileddemon?
Do you need to know the mass?[No, the velocity it needs to be to melt when it hits a wall]

19. Oct 31, 2006

### twotaileddemon

And.. it makes sense other than the heat of fusion part because I'm just learning it now. .thanks ^_^;

20. Oct 31, 2006

### marcusl

Sorry, we're using different terms. You call energy/(unit mass) the latent heat, I learned to call it specific latent heat. By that definition
latent heat = specific latent heat * mass
and that gives the equation I supplied.

I don't know which is formally proper, nor which is more commonly used...