3. a 16 kg barrel is lifted up by a rope. the barrel accelerates at 1.4 m/s2. find the force exerted by the rope. show all your work.

Net force = (mass) x (acceleration)

There are two forces acting on the barrel:

-- the force of gravity, downward;
-- the force of the rope, upward.

When these two forces are added together, their sum (the net force
on the barrel) causes the barrel to accelerate upward at 1.4 m/s² .
 
  Net force = (Rope force) - (Grav force) = (mass) x (acceleration)

Grav force = 'weight' = (mass) x (grav) = (16 x 9.8) =  156.8 newtons

Net force = (mass x acceleration) = (16 x 1.4) = 22.4 newtons

Net force =

                         22.4 newtons = (Rope force) - (156.8 newtons)

Add 156.8 newtons to each side:  Rope force = 22.4 + 156.8 = 179.2 newtons

Pe = 1/2k(x)^2  and .05n/m = .05x10^-9m = x