Answer:
45N and 15N respectively..
Step-by-step explanation:
(i)
To draw a sketch of the bookshelf, we can represent the supports P and Q as vertical lines on a horizontal axis, with the length of the bookshelf indicated between them. The book is located at a distance of 25 cm from support Q.
[Sketch of bookshelf with supports P and Q, and book located at a distance of 25 cm from Q]
(ii)
We can use the principle of moments to calculate the forces at supports P and Q. The principle of moments states that the sum of the moments of the forces acting on an object about a pivot point is equal to zero. We can use this principle to calculate the forces at the supports P and Q by taking the pivot point as the center of the bookshelf (50 cm from P and 50 cm from Q).
The weight of the bookshelf is 30 N, and the weight of the book is 21 N. The distance from the pivot point to the book is 25 cm, and the distance from the pivot point to support P is 50 cm.
We can set up the following equations to represent the principle of moments:
Moments about pivot point = 0
(30 N * 50 cm) - (21 N * 25 cm) = 0
Solving for the force at support P, we get:
F_P = 45 N
We can also solve for the force at support Q by setting the moments about the pivot point equal to zero:
(30 N * 50 cm) + (21 N * 25 cm) = 0
Solving for the force at support Q, we get:
F_Q = 15 N
Therefore, the forces at supports P and Q are 45 N and 15 N, respectively.