divide both sides of the equation by mass, it divides out.

mass*HeatFusion=mass*gh

How do you calculate the height that a block of ice at 0°C must be dropped to completely melt upon impact. Assume that all of the initial gravitational potential energy of the block goes into melting the ice.

ENergy to melt: mass*HeatofFusion
energ from falling: mass*g*h
set them equal, and solve for height h.

Watch your units.

Yeah, but we are not given mass. And it says that it is not needed. This is what totally throws me off. I don't see how I can solve without having mass.

Allie,you should rewrite the problem at the top so he can see it because I don't think he goes down again.LOL!Also,do you go to Gateway?Becuase I think I know you!

Explain Bot Explain Bot answered
9 months ago

To calculate the height at which a block of ice at 0°C must be dropped to completely melt upon impact, you can use the principle of conservation of energy.

First, consider the energy required to melt the ice. This can be calculated using the formula: energy to melt = mass * Heat Fusion, where mass is the mass of the ice and Heat Fusion is the heat of fusion for the ice, which is the amount of energy required to convert a unit mass of ice into water at 0°C.

Next, consider the energy gained by the block as it falls. This is given by the formula: energy from falling = mass * g * h, where g is the acceleration due to gravity and h is the height at which the block is dropped.

Since all of the initial gravitational potential energy of the block goes into melting the ice, the energy gained from falling must be equal to the energy required to melt the ice. Therefore, we can set up the following equation:

mass * Heat Fusion = mass * g * h

By dividing both sides of the equation by mass, we get:

Heat Fusion = g * h

Now, the question states that the mass of the ice is not needed. This means that the mass cancels out on both sides of the equation, and we can solve for the height h without knowing the mass.

To solve for h, rearrange the equation:

h = Heat Fusion / g

Make sure to use consistent units for Heat Fusion and g. For example, if Heat Fusion is given in Joules per gram and g is given in meters per second squared, make sure to convert them to the same units before calculating h.

I hope that helps! Let me know if you have any further questions.