Frozen waste from airplane toilets is routinely ejected at high altitude. Ordina

Question

Frozen waste from airplane toilets is routinely ejected at high altitude. Ordinarily it breaks up and disperses over a large area, but sometimes it holds together and strikes the ground. a. Calculate the mass of 0 o C ice that can be melted by the conversion of kinetic and gravitational potential energy to heat energy when the 20-kg piece of frozen waste is released at 12.0 km altitude while moving at 250 m/s and strikes the ground at 100 m/s. Assume that the local acceleration of gravity is constant over the entire trajectory. Also assume that the transfer to heat energy is 100 % efficient.

Explanation / Answer

Latent heat of fusion of ice, Lf = 334 KJ/Kg
Let mass of ice that can be melted be m Kg

Amount of mechanical energy converted to heat,
Q = initial kinetic energy - final kinetic energy + initial gravitational potential energy
= 0.5*20*250^2 - 0.5*25*100^2 +20*9.8*12000
=625000 - 125000 + 2352000
=2852000 J
= 2852 KJ

For ice melting,
Q = m*Lf

equate both Q
m*Lf = 2852
m* 334 = 2852
m = 8.54 Kg
Answer: 8.54 Kg

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.