Question

A bookshelf is 2m long, with supports at its end (p and q). A book weighing 10N is placed in the middle of the shelf. what are the upward forces acting on p and q. if the book is moved 50 cm from q, what are the forces at p and q now?

Answer 1

Fq = 2.5N

Fp = 7.5N

Step-by-step explanation:

Hello! Let's solve this!

When the book is in the middle, the force in p (Fp) and the force in q (Fq) are equal, and half of the total force

Fp = Fq = 5N

When the book moves 0.5m from q we have a balance

Fq * 2m = 10N * 0.5m

We cleared Fq

Fq = (10N * 0.5m) / 2m

Fq = 2.5N

Fp = 10N-Fq = 10N-2.5N = 7.5N

Conclusion

Fq = 2.5N

Fp = 7.5N

Answer 2

When the book is placed in the middle, the forces acting on p and q is 5N. When the book is moved 50 cm from q, the forces at p and q can be solved by doing a moment balance
With p as the pivot
Fq (2 m) = 10 N (0.5 m)
Fq = 2.5 N
and
Fp = 10 N - 2.5 N = 7.5 N