Question

A bookshelf is 2 m long, with supports at its ends (P and Q).

a)A book weighing 10 N is placed in the middle of the shelf. What are the upward forces at P and Q?
b)The book is moved so that it is 50 cm from Q. Use moments to calculate P the forces at P and Q.
c)The bookshelf weighs 10 N. Repeat parts b and taking into account
weight of the shelf as well as the weight of the book.

Answer 1

a) P + Q = 2 P = 10 N P = Q = 5 N each exerts the same force

b) P x1 = Q x2 if x1 and x2 are not equal (torque about pivot point)

50 Q = 150 P or Q = 3 P balancing torques

Since P + Q = 10 Q = 7.5 N and P = 2.5 N

c) take torques about P

100 * 10 + 100 * 10 = 200 * Q

Q = 10 N P + Q = 20 N upward and the force on the fulcrum in the middle is 10 + 10 = 20 N down (10 N for shelf and 10 N for book)