Question

Q10:

A room contains a book, a chair, a bookshelf, and a hatch that leads to a basement, as show in the diagram. The book has a weight of 7.5 N The seat of the chair is 0.45 m above the floor of the room, the bookshelf is 1.5 m above the floor of the room, and the basement floor is 2.2 m below the floor of the room. The book is placed in various positions and its gravitational potential energy changes depending on its position.
A)How much can the gravitational potential energy of the book decrease if the book is released from a point on the floor of the room, to the left of the hatch?
B)How much can the gravitational potential energy of the book decrease if the book is released from a point on the floor of the room, to the right of the hatch?
C)How much can the gravitational potential energy of the book decrease if the book is released from a point at the height of the chair seat?
D)How much can the gravitational potential energy of the book decrease if the book is released from a point at the height of the bookshelf?

Answer 1

To calculate the change in gravitational potential energy of the book as it falls from different starting points, we need to use the formula:

ΔPE = mgh

where ΔPE is the change in gravitational potential energy, m is the mass of the book, g is the gravitational acceleration (9.81 m/s^2), and h is the change in height.

A) If the book is released from a point on the floor of the room to the left of the hatch, it will fall towards the hatch and then fall further towards the basement floor. The change in height is the distance from the floor to the basement floor, which is 2.2 meters. Therefore, the change in gravitational potential energy is:

ΔPE = (7.5 N) x (9.81 m/s^2) x (2.2 m) = 162.8 Joules

B) If the book is released from a point on the floor of the room to the right of the hatch, it will fall towards the hatch and then fall further towards the basement floor as well. Therefore, the change in gravitational potential energy is the same as in Part A:

ΔPE = (7.5 N) x (9.81 m/s^2) x (2.2 m) = 162.8 Joules

C) If the book is released from a point at the height of the chair seat (0.45 m above the floor), it will fall towards the hatch and then fall further towards the basement floor. The change in height is the distance from the chair seat to the basement floor, which is:

h = 0.45 m + 2.2 m = 2.65 m

Therefore, the change in gravitational potential energy is:

ΔPE = (7.5 N) x (9.81 m/s^2) x (2.65 m) = 187.8 Joules

D) If the book is released from a point at the height of the bookshelf (1.5 m above the floor), it will fall directly towards the basement floor. The change in height is the distance from the bookshelf to the basement floor, which is:

h = 1.5 m + 2.2 m = 3.7 m

Therefore, the change in gravitational potential energy is:

ΔPE = (7.5 N) x (9.81 m/s^2) x (3.7 m) = 268.4