Question

Two movers are carrying a 4.0 m long sofa with a uniform distribution of mass along its entire length. One of them is standing all the way at one end, and provides a 350 N upward vertical force F1. The other is standing halfway between the midpoint and the other end. Fg is in the center! a. What is the force F2 needed at this location to prevent the sofa from rotating? b. What is the mass of the sofa?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the sofa = M

Length of the sofa = L = 4 m

Force applied by the first mover on the sofa = F₁ = 350 N

Force applied by the second mover on the sofa = F₂

The sofa has uniform mass distribution therefore the center of gravity of the sofa lies at the midpoint of it's length.

Distance of the first mover from the center of gravity of the sofa = D₁ = 2 m

The second mover is halfway between the midpoint and the other end.

Distance of the second mover from the center of gravity of the sofa = D₂ = 1 m

Taking moment balance about the center of gravity.

F₁D₁ = F₂D₂

(350)(2) = F₂(1)

F₂ = 700 N

Balancing all the forces on the sofa,

Mg = F₁ + F₂

M(9.81) = 350 + 700

M = 107 kg

a) Force applied by the second mover at the location to prevent the sofa from rotating = 700 N

b) Mass of the sofa = 107 kg