A 4.0-g sample of ice at 0.0 °C falls through a distance of 30.0 m and undergoes a completely inelastic collision with the earth. If all of the mechanical energy is absorbed by the ice, how much of it melts? A)2.9 × 10^-³ g B)3.3 × 10^-³ g C)7.6 × 10^-³ g D)1.8 × 10^-² g E)2.1 × 10^-² g

Question

Quizplus · Accepted Answer

The mechanical energy of the ice at the top of its fall is converted to heat energy during the inelastic collision with the earth. This heat energy will be used to melt some of the ice. To determine the amount of ice melted, we can use the conservation of mechanical energy:
PE = KE
mgh = (1/2)mv^2 
where m is the mass of the ice, h is the height it fell, v is its velocity just before the collision, g is the acceleration due to gravity, and PE and KE are the potential and kinetic energy of the ice, respectively. 
Solving for v, we get:
v = sqrt(2gh)
Plugging in the values, we get:
v = sqrt(2*9.8 m/s^2 * 30.0 m) = 24.2 m/s
The kinetic energy just before the collision is therefore:
KE = (1/2)mv^2 = (1/2)(0.004 kg)(24.2 m/s)^2 = 2.2 J
All of this energy is used to melt some of the ice. To find out how much, we can use the latent heat of fusion of ice, which is 334 J/g. 
The amount of ice melted is then:
melted = KE/latent heat of fusion = 2.2 J / 334 J/g = 0.0066 g
Therefore, the answer is B, 3.3 × 10^-3 g (rounded to two significant figures to match the given answer choices).

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