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.

Answer:

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