A baby elephant is stuck in a mud hole. To help pull it out,game keepers use a rope to apply force FA, as part(a) of the drawing shows. By itself, however, forceFA is insufficient. Therefore, two additionalforces FB and FC are applied, as in part (b)of the drawing. Each of these additional forces has the samemagnitude F and is oriented at θ = 20.00away from FA. The magnitude of the resultant forceacting on the elephant in part (b) of the drawing is twice that part a. Find the ratio F/FA.

Question

A baby elephant is stuck in a mud hole. To help pull it out,game keepers use a rope to apply force FA, as part(a) of the drawing shows. By itself, however, forceFA is insufficient. Therefore, two additionalforces FB and FC are applied, as in part (b)of the drawing. Each of these additional forces has the samemagnitude F and is oriented at θ = 20.00away from FA. The magnitude of the resultant forceacting on the elephant in part (b) of the drawing is twice that part a. Find the ratio F/FA.

Answer 1

To find the ratio F/FA, we need to first understand the forces acting on the elephant and use vector addition to determine the resultant force.

In part (a) of the drawing, only force FA is applied to pull the baby elephant out of the mud hole. Let's denote the magnitude of FA as FA.

In part (b) of the drawing, two additional forces, FB and FC, are applied. Both of these forces have the same magnitude F and are oriented at an angle of θ = 20.00 away from FA.

Since the magnitude of the resultant force in part (b) is stated to be twice that of part (a), we can represent it as 2FA.

Now, we can use vector addition to find the resultant force acting on the elephant in part (b). The resultant force is the vector sum of FA, FB, and FC.

We can break down FB and FC into their horizontal and vertical components using trigonometry. Since both FB and FC are at an angle of θ = 20.00 away from FA, their horizontal components will cancel each other out, and the vertical components will add up.

The vertical component of each force, FB and FC, can be calculated as F * sin(θ) = F * sin(20.00°).

Since the vertical components of FB and FC add up to give 2FA, we can write the equation as:

2FA = FB vertical component + FC vertical component
2FA = 2 * F * sin(20.00°) (Since FB and FC have the same magnitude and are at the same angle)

Now, we can solve for the ratio F/FA by rearranging the equation:

2FA = 2 * F * sin(20.00°)
FA = F * sin(20.00°)

Dividing both sides of the equation by FA, we get:

1 = sin(20.00°)

To find the value of sin(20.00°), you can use a scientific calculator or refer to a trigonometric table. Once you find the value, you can substitute it back into the equation to determine the ratio F/FA.