Question

A uniform rod is 2.00m long and has mass 2.20kg. A 2.80kg clamp is attached to the rod.

Part A

How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.30m from the left-hand end of the rod?

Express your answer with the appropriate units.

Answer 1

let left end is at origin

let m1 = 2.2 kg
coardinte of center of mass rod, x1 = L/2 = 2/2 = 1m

let m2 = 2.8 (mass of clamp)

xcm or Xcg = 1.3 m (since center of mass and center of gravity is same)

let x2 is the coardinate of center of gravity of clamp

x2 = ?

Apply, xcm = (m1*x1 + m2*x2)/(m1+m2)

Xcm*(m1+m2) = m1*x1 + m2*x2

x2 = (Xcm*(m1+m2) - m1*x1)/m2

= (1.3*(2.2+2.8) - 2.2*1)/2.8

= 1.536 m <<<<<<<<-------------Answer