If you drop a piece of ice on a hard surface, the energy of impact will melt some of the ice. The higher it drops, the more ice will melt upon impact.Find the height from which a block of ice should ideally be dropped to completely melt it that falls without air drag.
[Hint: Equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (in SI units, 335,000 J/kgDo you see why the answer doesn't depend on mass?]
34,000m
34 km
Nooo
To determine the height from which a block of ice should ideally be dropped to completely melt it without air drag, we can use the principle of conservation of energy.
The potential energy (PE) of an object in a gravitational field is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
The energy needed to melt a specific mass of ice is given by the formula E = m × L, where L is the heat of fusion (335,000 J/kg for ice in this case).
As per the hint, we can equate the potential energy to the energy required to melt the ice:
mgh = mL
We can cancel out the mass (m) from both sides of the equation, as the mass of the ice does not affect the height from which it should be dropped. This happens because the mass cancels out from both sides of the equation.
Therefore, the equation becomes:
gh = L
Solving for h gives us:
h = L/g
Plugging in the values for L (335,000 J/kg) and g (9.8 m/s^2), we can find the height from which the ice should be dropped:
h = 335,000 J/kg / 9.8 m/s^2
h ≈ 34,184 meters
Therefore, the ice should ideally be dropped from a height of approximately 34,184 meters to completely melt upon impact without considering air drag.