Newton's 2nd Law Force Problem

[BrainHurtsxyz]

Homework Statement

There are two forces on the 1.97 kg box in the overhead view of Fig. 5-31 but only one is shown. For F1 = 27.6 N, a = 11.1 m/s2, and θ = 31.9°, find the second force (a) in unit-vector notation and as (b) a magnitude and (c) a direction. (State the direction as a negative angle measured from the +x direction.)

The diagram shown is a Box with F1 ------> and acceleration pointing 31.9 degrees southwest of the Y-axis.

Homework Equations

F2= mx - F1

The Attempt at a Solution

No idea... I first tried to solve for the x and y component of the above equation and I wound up getting a messed up answer.

 

[anathema]

Then I tried to use the Pythagorean theorem and inverse tangent to solve for the magnitude and direction but that also didn't work. Can someone please help me understand how to solve this problem?
Thank you for your question. Based on the information provided, it seems like you are trying to solve for the second force acting on the box in the overhead view. To do this, we can use Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, we have two forces acting on the box: F1 and F2. We can write this as the following equation:

ΣF = m*a

Where ΣF is the sum of all the forces acting on the box, m is the mass of the box, and a is its acceleration.

Now, let's break down the forces into their x and y components. F1 is already given in unit-vector notation, so we can simply write it as:

F1 = 27.6 N (cos 31.9° i + sin 31.9° j)

To find F2, we need to use the equation you mentioned: F2 = m*a - F1. Since we know the mass and acceleration of the box, we can plug in those values and solve for F2. This will give us the x and y components of F2.

Once we have the x and y components of F2, we can use the Pythagorean theorem to find its magnitude, and inverse tangent to find its direction. Remember to include the negative sign in the direction, as it is measured from the +x direction.

I hope this helps you understand how to solve this problem. Let me know if you have any further questions. Good luck with your studies!
Scientist