Question

A 5 meter long plank has a mass of 4 kg. It is supported by 2 supports, the
first at 1 meter from the end, and the second at 3 meters from that same end.
How much upward force is supplied by the second support?

Answer 1

it is uniform plank so the centre of mass acts at the distance 2.5m .

let reaction at support 1 is x and support 2 is y.

(1) force balance;

so x+y - 4*10 = 0

x+y=40

(2)momentum balance;

balance at support 1

x*0 + y*2 - 40*1.5 =0

2y =60

y=30 N

so the reaction at second support = 30 N and at the first support = 40-30 =10 N