A 3.0-kg mass is dropped from the edge of a 50-m tall building with an initial speed of zero.The mass strikes the ground with a downward velocity of 25 m/s.Find the change in mechanical energy of the mass caused by air resistance between the point where it is dropped and the point where it strikes the ground?
A)-0.46 kJ
B)-0.53 kJ
C)-0.61 kJ
D)-0.38 kJ
E)-0.81 kJ

Question

Quizplus · Accepted Answer

The change in mechanical energy is equal to the work done by air resistance. We can calculate the potential energy of the mass before it falls using the equation: 
PE = mgh = (3.0 kg)(9.8 m/s^2)(50 m) = 1470 J

At the point of impact, the mass has lost all of its potential energy and gained kinetic energy: 
KE = (1/2)mv^2 = (1/2)(3.0 kg)(25 m/s)^2 = 937.5 J

Therefore, the change in mechanical energy is: 
ΔE = KE - PE = 937.5 J - 1470 J = -532.5 J

Since the mass has lost mechanical energy due to air resistance, the answer must be negative. The closest option is B: -0.53 kJ or -530 J, which represents a loss of 530 J of mechanical energy.

A 30-Kg Mass Is Dropped from the Edge of a 50-M