Question

A baby elephant is stuck in a mud hole. To help pull it out, game keepers use a rope to apply a force Fa, as part a of the drawing shows. By itself, however, Fa force is insufficient. Therefore, two additional forces Fb and Fc are applied, as in part b of the drawing. Each of these additional forces has the same magnitude F. The magnitude of the resultant force acting on the elephant in part b of the drawing is k times larger than that in part a. Find the ratio F/FA when k = 2.00.

Answer 1

When k = 2.00, the ratio F/FA is -1/4.

Step-by-step explanation:

To find the ratio F/FA when k = 2.00, we can use vector addition principles. In part a of the drawing, the force applied is only Fa. In part b, there are three forces acting on the baby elephant: Fa, Fb, and Fc. We need to find the magnitude of the resultant force R in both cases and then calculate the ratio F/FA.

Part a: Only Fa is acting.

In this case, R is equal to Fa itself because there are no other forces to consider.

R_a = Fa

Part b: Fa, Fb, and Fc are acting.

In this case, we can use the concept of vector addition to find the resultant force R_b. The resultant of these three forces can be found as the vector sum:

R_b = Fa + Fb + Fc

Given that each of these additional forces Fb and Fc has the same magnitude F, we can rewrite the equation as:

R_b = Fa + F + F

Now, we know that the magnitude of the resultant force R_b is k times larger than that in part a, where k = 2.00:

R_b = 2 * R_a

Substituting R_a and R_b:

Fa = 2 * (Fa + F + F)

Now, solve for F:

Fa = 2 * (Fa + 2F)

Divide both sides by 2:

Fa/2 = Fa + 2F

Subtract Fa from both sides:

-Fa/2 = 2F

Now, isolate F:

F = -Fa/4

So, the ratio F/FA is:

F/FA = (-Fa/4) / Fa

F/FA = -1/4

When k = 2.00, the ratio F/FA is -1/4.