(Score for Question 3: ___ of 8 points) A 75 kg barrel is pulled up by a rope. The barrel accelerates at 3".4 m"/s^2. Find the force exerted on the barrel by the rope. Show all your work.

Type your answer here.

255N

Explanation:

Given parameters:

Mass of barrel  = 75kg

Acceleration  = 3.4m/s²

Unknown:

Force exerted  = ?

Solution:

Force is the product of mass and acceleration according to Newton's second law of motion.

  Force  = mass x acceleration

Now insert given parameters and solve,

       Force  = 75 x 3.4  = 255N

The net force on the barrel is the sum of the pulling force (magnitude p, acting upward) and the barrel's weight (mag. w, opposing p ). So by Newton's second law,

∑ F = p - w = m a

p = w + m a

p = m g + m a

p = m (g + a)

p = (75 kg) (9.80 m/s² + 3.4 m/s²)

p = 990 N

the diagram which shows forces as either balanced = same speed or unbalanced = accelerarting