A book has a weight of 13 N and is allowed to drop from a height of 19 m.

Question

Calculate the gravitational potential energy before the book is dropped.

 

Calculate the kinetic energy of the book when it has fallen half way to the ground.

 

Calculate the gravitational potential energy when it has fallen half way to the ground.

 

Calculate the kinetic energy of the book the moment before it reaches the ground.

Answer 1

(part 1) PEg = mgh = mg(h), where mg = Fg == weight

So, PEg = weight * h

Plugging in the numbers, a book with weight of 13 N at height of 19 m has

PEg(at 19 m) = 13N * 19m = 247 N-m (PEg before book is dropped)

≈ 250 N-m (2 sig figs) (ANSWER 1)

(part 2) After it has fallen half-way, the height is half-way, but the weight is the same, so

PEg(at 9.5 m) = 13N * 9.5 m = 0.5 * 247 N-m = 123.5 N-m

≈ 120 N-m (2 sig figs)

PE + KE == constant (Law of conservation of Energy)

PE has dropped by 1/2, KE = 0 before the book was dropped, so

KE (at 9.5 m) ≈ 120 N-m (2 sig figs) (ANSWER 2)

(part 3) Just before it reaches the ground, all of the PEg(at 19 m) has been converted into KE

because of the Law of conservation of energy, so

KE(just before it hits the ground) == PEg(at 19 m), so

≈ 250 N-m (2 sig figs) (ANSWER 3)