. Two people pull on a stubborn mule, as seen from a helicopter in Figure 2.1. Find (a) the single force that is equivalent to the two forces shown, and (b) the force that a third person would have to exert on the mule to make the net force equal to zero.

I don't know what Fig. 2.1 looks like.

single force equivalent of the two forces is a magnitude of 190.1696 N

The direction is 75.9 degrees counterclockwise

the force a 3rd person would have to exert to make the net force zero is 188.48 N

To solve this problem, we can use vector addition to find the equivalent force and the force needed to make the net force zero.

(a) To find the single force that is equivalent to the two forces shown, we need to add the two forces together.

Let's assume that the force exerted by the first person is F1, and the force exerted by the second person is F2.

To find the equivalent force, we can use the formula:

Resultant force (F3) = F1 + F2

(b) To find the force that a third person would have to exert on the mule to make the net force equal to zero, we need to calculate the negative of the sum of the two forces.

Let's denote the force needed as F3.

To make the net force zero, we have:

F1 + F2 + F3 = 0

Now we can proceed to calculate the values:

(a) To find the single force equivalent to the two forces shown, you can add the forces together:

F3 (Resultant force) = F1 + F2

(b) To find the force that a third person would have to exert on the mule to make the net force equal to zero, we need to calculate the negative of the sum of the two forces:

F1 + F2 + F3 = 0

Therefore, to make the net force zero, the force needed would be:

F3 = -(F1 + F2)

To find the single force that is equivalent to the two forces shown, we need to use vector addition. The vector addition can be done graphically or analytically using trigonometry.

(a) Graphical method:
1. Draw a scale diagram of the two forces. Represent each force as an arrow with its magnitude and direction.
2. Place the tail of the second force (force exerted by the second person) at the head of the first force (force exerted by the first person).
3. Draw an arrow from the tail of the first force to the head of the second force. This arrow represents the net force.
4. Measure the magnitude and direction of the net force using a ruler and protractor. This will give you the single force equivalent to the two forces.

(b) Analytical method:
1. Resolve each force into its horizontal and vertical components. To do this, multiply the magnitude of each force by the cosine of the angle it makes with the horizontal axis to find its horizontal component and by the sine of the angle to find its vertical component.
2. Add the horizontal components of the two forces to find the net horizontal force.
3. Add the vertical components of the two forces to find the net vertical force.
4. Use the calculated horizontal and vertical net forces to find the magnitude and direction of the net force using the Pythagorean theorem and trigonometry.

To make the net force equal to zero, a third person would have to exert a force equal in magnitude and opposite in direction to the net force calculated in part (a).