The Weistin Stamford Hotel in Detroit is 228 m tall. Suppose a piece of ice which initially has a temperature of o degrees celcius falls from the hotel roof and crashes to the ground. Assuming that 50% of the ices mechanical energy during the fall and collision is absorbed by the ice and that 3.33 x 10^5 Joules is required to melt 1 kg of ice calculate the fraction of ice's mass that would melt.

Question

The Weistin Stamford Hotel in Detroit is 228 m tall. Suppose a piece of ice which initially has a temperature of o degrees celcius falls from the hotel roof and crashes to the ground. Assuming that 50% of the ices mechanical energy during the fall and collision is absorbed by the ice and that 3.33 x 10^5 Joules is required to melt 1 kg of ice calculate the fraction of ice's mass that would melt.

Answer 1

Compute the potential energy release of the fall (Hint: PE = Mgh). The mass M will remain as an unknown variable. Multiply that by 0.5 for the heat release. Divide the result by the heat of fusion (33.5*10^5 J/kg x M)

The mass M will cancel out, and you will have the fraction that melts.

Answer 2

To calculate the fraction of the ice's mass that would melt, we need to consider the energy involved in the fall and collision as well as the energy required to melt the ice.

First, let's calculate the potential energy that the ice gains during the fall. The potential energy (PE) is given by the equation PE = mgh, where m is the mass of the ice, g is the acceleration due to gravity, and h is the height.

Given:
Height (h) = 228 m
m = mass of the ice

Next, let's calculate the total mechanical energy (E_total) of the ice, considering that 50% of it is absorbed during the fall and collision. The mechanical energy (E) is given by the equation E = PE. Since half of the mechanical energy is absorbed, E_total = 0.5 * E.

E_total = 0.5 * mgh

Now, let's calculate the mass of the ice that melts using the energy required to melt 1 kg of ice (energy_per_kg). The fraction of the ice's mass that melts can be calculated using the equation:

Fraction of mass melted = E_total / (energy_per_kg * m)

Given:
Energy required to melt 1 kg of ice (energy_per_kg) = 3.33 x 10^5 Joules

Fraction of mass melted = (0.5 * mgh) / (energy_per_kg * m)

Using the given height of the Weistin Stamford Hotel (228 m) and the energy required to melt 1 kg of ice (3.33 x 10^5 J), you can substitute these values into the equation to calculate the fraction of the ice's mass that would melt.

Note: The mass of the ice (m) is not provided in the question. To find the exact fraction of the ice's mass that would melt, you would need to know the mass of the ice.