Calculate the height from which a block of ice at zero degrees celcius nust be dropped for it to completely melt upon impact. Assume that there is no air resistance and that all the energy goes into melting the ice.
m g h = 334*10^3 joules/kg * m
h = 334*10^3/9.81 in meters
0°c ice converted to 0°c water
mlf=m×3.36×10^5
Work done=heat produced
or,mgh=mlf
or,gh=lf
or,h=3.36×10^5÷9.8
or,h=34.286×10^3
To calculate the height from which a block of ice must be dropped for it to completely melt upon impact, we can use the concept of potential energy and energy conservation.
First, let's consider the energy involved in this scenario. The block of ice will gain potential energy as it falls from a certain height, and this potential energy will then be converted into thermal energy to completely melt the ice.
The potential energy (PE) of an object is given by the equation: PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
The energy required to completely melt the ice is called the heat of fusion. For ice to water at its melting point, it requires 334,000 J/kg.
So, to calculate the height from which the block of ice must be dropped, we equate the potential energy with the heat of fusion:
m * g * h = m * Hf
The mass of the ice cancels out on both sides of the equation, leaving:
g * h = Hf
Simplifying further, we find:
h = Hf / g
Now substitute the heat of fusion value for water:
h = 334,000 J/kg / 9.8 m/s^2
Calculating this gives:
h ≈ 34,082.̅1 kg·m^2/s^2 ≈ 34,082 m
Therefore, the height from which the block of ice must be dropped for it to completely melt upon impact is approximately 34,082 meters (34.1 kilometers).