calculate the height a block of ice at -25 deg C must be dropped in order to completely melt on impact. No air resistance and all energy goes into melting the ice.
Depends upon how much ice you have? How much does a block of ice weigh?
To calculate the height at which the block of ice must be dropped in order to completely melt on impact, we need to consider the energy required for melting and the potential energy gained by the block as it falls.
The energy required to completely melt the ice can be calculated using the equation:
Q = m * L
where Q is the heat energy required, m is the mass of the ice, and L is the latent heat of fusion, which is the heat energy required to change a substance from solid to liquid at a constant temperature.
The potential energy gained by the block as it falls can be calculated using the equation:
PE = m * g * h
where PE is the potential energy, m is the mass of the ice, g is the acceleration due to gravity (9.8 m/s^2), and h is the height from which it is dropped.
For the ice to completely melt, the heat energy gained while falling must equal the energy required for melting. Therefore, we can set the two equations equal to each other:
m * g * h = m * L
We can cancel out the mass (m) on both sides of the equation, giving us:
g * h = L
Now we can solve for h:
h = L / g
Now let's plug in the values. The latent heat of fusion of ice is approximately 334,000 J/kg, and the acceleration due to gravity is 9.8 m/s^2:
h = 334,000 J/kg / 9.8 m/s^2
Calculating this gives us:
h ≈ 34,082 meters
Therefore, the block of ice must be dropped from a height of approximately 34,082 meters (34.082 kilometers) in order to completely melt on impact, assuming no air resistance and that all the energy goes into melting the ice.