Assume all temperatures to be exact. A 0.030-kg lead bullet hits a steel plate,

Question

Assume all temperatures to be exact. A 0.030-kg lead bullet hits a steel plate, both initially at 20 C. The bullet melts and splatters on impact. (This action has been photographed.)

a) Assuming that 72 % of the bullet's kinetic energy goes into increasing its temperature and then melting it, what is the minimum speed it must have to melt on impact? Express your answer using two significant figures.

b) A waterfall is 75 m high. If 20% of the gravitational potential energy of the water went into heating the water, by how much would the temperature of the water, increase in going from the top of the falls to the bottom? [Hint: Consider a kilogram of water going over the falls.]

c) When you go out to your car one cold winter morning you discover a 0.80-cm thick layer of ice on the windshield, which has an area of 1.2 m2 . If the temperature of the ice is -5.0 C, and its density is 917 kg/m3, find the heat required to melt all the ice.

Explanation / Answer

a) KE of bullet = 0.030v2 / 2 = 0.015v2

Now,

0.72 * 0.015v2 = 0.030 * [(128 * (327.5 - 20)) + 23000]

=> v = 416.2 m/s = 420 m/s (upto 2 significant figures)

b) Q = mCwT = 0.2mgh

=> T = 0.2gh/Cw = 0.2 * 9.81 * 75 / 4184 = 0.035 oC

c) Q = m(L + CT) = (1.2 * 0.8 * 10-2) * 917 * [334000 + (2050 * 5)] = 3.03 * 106 J

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