physics question

Question

The helicopter view in the figure below shows two people pulling on a stubborn mule. (Take F₁ = 143 N and F₂ = 73.0 N.)

(a) Find the single force that is equivalent to the two forces shown

Magnitude____?____

Direction_____?____ ° counterclockwise from the +x-axis

(b) Find the force a third person would have to exert on the mule to make the net force equal to zero.

Magnitude _____?______ N

Direction ______________ ° counterclockwise from the +x-axis

Answer 1

Since you didn't show the figure, there is no way of doing the problem. But here's how you would do it.

Break the 2 vectors up into their x-components and y-components using sine and cosine ratios like this:

Add the two x-components:

F_Total(x) = F₁cos(α) + F₂cos(β)

Add the two y-components (keeping in mind that the F2 y-component is negative because it is going downwards):

F_Total(y) = F₁sin(α) - F₂sin(β)

Recombine F_Total(x) and F_Total(y) into a vector with magnitude determined by the Pythagorean Theorem and direction determined by the tangent trig ratio:

F_{Total(magnitude)} = √((F_Total(x))² + (F_Total(y))²)

F_{Total(direction)} = tan^-1(F_Total(y)/F_Total(x))

Regarding the last question, the vector making a net zero would be equal in magnitude to the above but 180° off in direction.