Solving Vectors Problem: 4 People Pulling on Rope at Square Corners

[myoplex11]

Homework Statement

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

Homework Equations

The Attempt at a Solution

Fx = 17cos60+11cos60-11cos60-15cos60
Fy = 17sin60-11sin60-11sin60+15sin60
fnet = (fx^2+fy^2)^.5
i am not getting the right anwser where am i going wrong

 

[alphysicist]

Hi myoplex11,

Homework Statement

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

Homework Equations

The Attempt at a Solution

Fx = 17cos60+11cos60-11cos60-15cos60
Fy = 17sin60-11sin60-11sin60+15sin60
fnet = (fx^2+fy^2)^.5
i am not getting the right anwser where am i going wrong

I don't believe the angles involved here are 60 degrees. What would they be?

 

[baba89]

Your approach is correct, but there are a few errors in your calculations. Here is a step-by-step solution:

1) First, let's find the x and y components of each force:

- Fred: Fx = 11*cos(45°) = 7.778 N, Fy = 11*sin(45°) = 7.778 N
- Ted: Fx = 11*cos(135°) = -7.778 N, Fy = 11*sin(135°) = 7.778 N
- Ed: Fx = 17*cos(225°) = -12.02 N, Fy = 17*sin(225°) = -12.02 N
- Ned: Fx = 15*cos(315°) = 10.606 N, Fy = 15*sin(315°) = -10.606 N

2) Next, let's sum up the x and y components to get the net force in each direction:

- Fx = 7.778 N - 7.778 N - 12.02 N + 10.606 N = -1.414 N
- Fy = 7.778 N + 7.778 N - 12.02 N - 10.606 N = -6.07 N

3) Now, we can find the magnitude and direction of the net force using the Pythagorean theorem and inverse tangent function:

- Magnitude: Fnet = √((-1.414 N)^2 + (-6.07 N)^2) = 6.267 N
- Direction: θ = tan^-1(-6.07 N / -1.414 N) = 76.145° or 286.145° (measured counterclockwise from the positive x-axis)

Therefore, the net force exerted on the center point is 6.267 N at an angle of 76.145° or 286.145° from the positive x-axis.

Hope this helps!