Problem 2P

What is the approximate mass of air in a living room 4.8 m × 3.8 m × 2.8 m?

ANSWER: The mass of the book is 2 kg. The height of the table is 0.75 m. When you lift the book upwards, the work is done by you and considered as a positive work, because you did work against gravity. When you bring the book downward, the work is done by the book and also considered as negative work, because you did the work for gravity. These are the ways we have defined gravitational potential energy has defined. a) work done by gravity on the book You took the book to a bookshelf 2.3 m above the floor. So the net displacement for the book while taking it up is, 2.3 0.75 = 1.55 meters. The force you have applied on the book is, F = ma = 2 kg × 9.8 m/s = 19.6 N We know the work is, W = force × displacement = 19.6 N × 1.55 m = 30.38 jules The force is downward (gravity) and the displacement is upwards, so the cosine of the angle between them gives a minus sign. So while taking the book up you did a work of -30.38 jules. b) Work done by your hand on the book W = force × displacement = 19.6 N × 1.55 m = 30.38 jules The force is upward (by your hand) and the displacement is also upwards, so the cosine of the angle between them gives a plus sign. CONCLUSION: So the work done by gravity is -30.38 jules and the work done by your hand is +30.38 jules.