Problem 34P

A 5.25-kg piece of wood (SG = 0.50) floats on water. What minimum mass of lead, hung from the wood by a string, will cause it to sink?

ANSWER:The mass of the fireman is 80 kg.The total vertical displacement is 4.2 meter.The final speed just before reaching the bottom is 2.2 m/s.So,The initial kinetic energy was zero, as the initial velocity was zero.Initial potential energy is mgh = 80 × 9.8 × 4.2 = 3292.8 jules, as the height was 4.2 meters.. 2 2Final kinetic energy was 1/2 mv = 1/2 × 80 × 2.2 = 193.6 jules, where v is the velocity atthe bottom.Final potential energy is zero, as the height is zero.STEP 2:-After having all these values, let’s put them in the equation of mechanical energyconservation. K.E + P.E = K.E + P.E initial initial final final 0 + 3292.8 = 193.6 + 0But, 3292.8 = / 193.6So, there must be a loss in energy. Friction we cannot ignore here as we know it’s adissipative system whose energy got lost by the process.\nSo, the lost energy is not in the form of mechanical energy anymore. And we are notsupposed to use the law of conservation of mechanical energy. We must use the law ofconservation of energy, which is always true.The energy loss must have converted to thermal energy. Let’s find it.The thermal energy is, the forbidden mechanical energy, i.e; 3292.8 193.6 = 3099.2 = 3100 jules approximately.CONCLUSION:So, the increase in thermal energy due to the slide is 3100 jules.