Three people attempt to haul a heavy sign to the roof of a building by using three ropes attached to the sign. Abby stands directly above the sign and pulls straight up on a rope. Eric and Kim stand on either side of Abby. Their ropes form 30.0 degree angles with Abby’s rope. A force of 102 N is applied on each rope. What is the ent upward force acting on the sign?

To find the upward force acting on the sign, we need to determine the vertical components of the forces applied by each person.

First, let's consider Abby's force. Since she is pulling directly upward, the entire force she exerts will contribute to the upward force. Therefore, the vertical component of Abby's force is 102 N.

Now let's break down the forces applied by Eric and Kim. Since their ropes form 30.0 degree angles with Abby's rope, we can use trigonometry to find the vertical components.

The vertical component of a force can be found by multiplying the magnitude of the force by the cosine of the angle. So, for each person, the vertical component of their force is:

Vertical component = Force * cos(angle)

For Eric:
Vertical component of Eric's force = 102 N * cos(30.0°) = 102 N * 0.866 = 88.232 N (rounded to three decimal places)

For Kim:
Vertical component of Kim's force = 102 N * cos(30.0°) = 102 N * 0.866 = 88.232 N (rounded to three decimal places)

Now, to find the total upward force acting on the sign, we simply add the vertical components of all three forces:
Total upward force = Abby's force + Eric's force + Kim's force
Total upward force = 102 N + 88.232 N + 88.232 N = 278.464 N

Therefore, the total upward force acting on the sign is 278.464 N.

To find the net upward force acting on the sign, we need to resolve the forces along the vertical axis.

First, let's calculate the vertical component of the force exerted by Abby's rope. Since she is pulling straight up, the vertical component is equal to the total force of 102 N.

Next, we need to calculate the vertical components of the forces exerted by Eric and Kim. Since their ropes form angles of 30.0 degrees with Abby's rope, the vertical component of their forces can be obtained by multiplying the force by the sine of the angle.

Vertical component of force exerted by Eric = 102 N * sin(30.0°)
Vertical component of force exerted by Kim = 102 N * sin(30.0°)

Now, we add up the vertical components of the forces exerted by each person to find the net upward force acting on the sign:

Net upward force = Vertical force exerted by Abby + Vertical force exerted by Eric + Vertical force exerted by Kim
= 102 N + (102 N * sin(30.0°)) + (102 N * sin(30.0°))

Calculating this expression will give us the value of the net upward force acting on the sign.

T2 = T1*sin60 = 102*sin60 = 88.3 N.