4 people stand at the corners of a square. Fred stands at point (0,0)

Ted at (1,0) Ed at (1,1) and ned at (0,1). they each pull on a rope connected to the center of the square
(0.5,0.5). Fred exerts 11N, Ted exerts 11N, Ed 17N and Ned 15N. what is the net force exerted on the center point and what is the angle from the positive x-axis

Use symettry. If two are pulling from opposite corners, the net force in that direction is zero. If two are pulling from opposite corners with different forces, the net force is the difference.

If you draw this properly you will observe that along the Fred-Ed line you have a resultant of 6N toward Ed. Along the Ted-Ned line you have a resultant of 4N toward Ned.

If you combine the two new vectors graphically, you have a right triangle with the hypotenuse being the resultant. Use the Pythagorean Theorem to get the magnitude. To get the direction, D, use:
D = tan^-1(4/6)+ 45o
The above angle is measured from the Eastward direction upward (counterclockwise).

To find the net force exerted on the center point of the square, we need to calculate the horizontal and vertical components of the force exerted by each person.

First, let's find the horizontal component of the force exerted by each person:

Fred's horizontal component: 11N * cos(45°) = 11N * 0.7071 ≈ 7.778N
Ted's horizontal component: 11N * cos(45°) = 11N * 0.7071 ≈ 7.778N
Ed's horizontal component: 17N * cos(45°) = 17N * 0.7071 ≈ 12.020N
Ned's horizontal component: 15N * cos(45°) = 15N * 0.7071 ≈ 10.606N

Next, let's find the vertical component of the force exerted by each person:

Fred's vertical component: 11N * sin(45°) = 11N * 0.7071 ≈ 7.778N
Ted's vertical component: 11N * sin(45°) = 11N * 0.7071 ≈ 7.778N
Ed's vertical component: 17N * sin(45°) = 17N * 0.7071 ≈ 12.020N
Ned's vertical component: 15N * sin(45°) = 15N * 0.7071 ≈ 10.606N

To find the total horizontal and vertical components of the force, we can add up the respective components:

Total horizontal component: 7.778N + 7.778N + 12.020N + 10.606N = 38.182N
Total vertical component: 7.778N + 7.778N + 12.020N + 10.606N = 38.182N

Now, we can use these components to find the net force using the Pythagorean theorem:

Net force = √((Total horizontal component)^2 + (Total vertical component)^2)
= √((38.182N)^2 + (38.182N)^2)
≈ √(1458.7428N + 1458.7428N)
≈ √2917.4856N
≈ 53.975N

So, the net force exerted on the center point is approximately 53.975N.

The angle from the positive x-axis can be found using the inverse tangent (arctan) function:

Angle = arctan(Total vertical component / Total horizontal component)
= arctan(38.182N / 38.182N)
= arctan(1)
≈ 45°

Therefore, the angle from the positive x-axis is approximately 45°.

To find the net force exerted on the center point, we need to calculate the vector sum of all the individual forces.

Let's break down each force into its x and y components:

Fred: Force = 11N, x-component = 11N * cos(45°) = 7.778N, y-component = 11N * sin(45°) = 7.778N
Ted: Force = 11N, x-component = 11N * cos(135°) = -7.778N, y-component = 11N * sin(135°) = 7.778N
Ed: Force = 17N, x-component = 17N * cos(45°) = 12.021N, y-component = 17N * sin(45°) = 12.021N
Ned: Force = 15N, x-component = 15N * cos(135°) = -10.606N, y-component = 15N * sin(135°) = 10.606N

Now, let's sum up the x and y components:

Net x-component = 7.778N - 7.778N + 12.021N - 10.606N = 1.415N
Net y-component = 7.778N + 7.778N + 12.021N + 10.606N = 38.183N

Using the Pythagorean theorem, we can find the magnitude of the net force:

Net force = sqrt((Net x-component)^2 + (Net y-component)^2)
= sqrt((1.415N)^2 + (38.183N)^2)
≈ 38.53N

To find the angle from the positive x-axis, we can use trigonometry:

Angle = arctan(Net y-component / Net x-component)
= arctan(38.183N / 1.415N)
= arctan(27.01)
≈ 89.98°

Therefore, the net force exerted on the center point is approximately 38.53N, and the angle from the positive x-axis is approximately 89.98°.