Question

Two ropes are connected to a 200 kg dinghy. Two cousins each take one rope and pull. When the cousins pull in the same direction, the dinghy accelerates at a rate of 1.31 m/s2 to the east. If they pull in opposite directions, the dinghy has an acceleration of 0.526 m/s2 to the west. Assume the ropes are horizontal, and ignore any other horizontal forces acting on the dinghy. What is the magnitude of the force each cousin exerts on the dinghy

Answer 1

The magnitude of the force each cousin exerts on the dinghy is 183.6 N and 78.4 N.

Step-by-step explanation:

When the cousins pull in the same direction we have:

`F_(1) + F_(2) = ma_(e)` (1)

Where:

F₁ and F₂ are the forces exerted by the two boys.

m: is the mass of the dinghy = 200 kg

`a_(e)`: is the acceleration in the east direction

When the cousins pull in opposite directions we have:

`F_(1) - F_(2) = ma_(w)` (2)

By adding equation (1) and (2):

`2F_(1) = m(a_(e) + a_(w))`

`F_(1) = (200 kg(1.31 m/s^(2) + 0.526 m/s^(2)))/(2) = 183.6 N`

Now, by entering F₁ into equation (1) we can find F₂:

`F_(2) = ma_(e) - F_(1) = 200kg*1.31 m/s^(2) - 183.6 N = 78.4 N`

Therefore, the magnitude of the force each cousin exerts on the dinghy is 183.6 N and 78.4 N.

I hope it helps you!