The following free body diagram represents the forces acting on a barge being towed by tugboat into a

harbor.

Fbuoy = 25,000 N

Fpull = 350 N

Ffriction = 100 N

Fw = 25,000 N

What is the net force acting on the barge?

250 N to the left

100 N to the right

300 N to the right

350 N to the left

If the mass of the barge is 12,000 kg, what is the acceleration it experiences? (1 point)

0.981 m/s^2 to the right

0.021 m/s^2 to the left

3.91 m/s^2 to the left

0.067 m/s^2 to the right

1 answer

To determine the net force acting on the barge, we need to consider all the forces acting on it and their directions.

  1. Buoyant force (F_buoy): 25,000 N (upward)
  2. Pulling force (F_pull): 350 N (rightward)
  3. Friction force (F_friction): 100 N (leftward)
  4. Weight of the barge (Fw): 25,000 N (downward)

We can find the net horizontal force first:

  • The net horizontal force (F_net_horizontal) is given by the pulling force minus the friction force: \[ F_{net_horizontal} = F_{pull} - F_{friction} = 350 , \text{N} - 100 , \text{N} = 250 , \text{N} , \text{to the right} \]

Since vertical forces (buoyant and weight) do not affect horizontal motion, we focus on the horizontal forces.

Now, the net force acting on the barge is:

  • 250 N to the right.

Therefore, the answer to the first question is: 250 N to the right


Next, for the acceleration of the barge, we can use Newton's second law: \[ F_{net} = m \times a \] Where:

  • \( F_{net} \) is the net force (250 N to the right)
  • \( m \) is the mass of the barge (12,000 kg)
  • \( a \) is the acceleration

Reorganizing the equation to solve for acceleration: \[ a = \frac{F_{net}}{m} \] Substituting in the values: \[ a = \frac{250 , \text{N}}{12,000 , \text{kg}} \approx 0.02083 , \text{m/s}^2 \]

  • This round to 0.021 m/s².

Since the force is to the right, the acceleration will also be to the right.

Therefore, the answer to the second question is: 0.021 m/s^2 to the right.