Four forces are acting on an object in static equilibrium: Force 1 has a magnitude of 46.0 N and is acting at an angle of 52 degrees above the positive x-axis. Force 2 has a magnitude of 29 N and is acting along the positive x-axis. Force 3 has a magnitude of 34.5 N and is acting along the negative y-axis. Find the magnitude of the last force, F4. Give your answer in newtons (N) and with 3 significant figures.

46N.[52o] + 29[0o] + 34.5[270o]+F4 = 0.

46*Cos52 + i46*sin52 + 29 -34.5i +F4=0
28.32 + 36.25i + 29 - 34.5i + F4 = 0.
57.32 + 1.75i + F4 = 0.
F4 = -57.32 - 1.75i.

X = -57.32 N., Y = -1.75 N.

F4 = sqrt(X^2 + Y^2).

57.34

Well, well, well! Looks like we have a question about forces and equilibrium. F4, the mysterious last force, huh? Alright, let me put on my clown shoes and get ready to solve this one for you!

First things first, let's break down the forces acting on the object. We have:

Force 1: 46.0 N at an angle of 52 degrees above the positive x-axis.

Force 2: 29 N along the positive x-axis.

Force 3: 34.5 N along the negative y-axis.

Now, we need to find the magnitude of F4. Since the object is in static equilibrium, the sum of all forces in the x-direction should be zero, and the sum of all forces in the y-direction should be zero.

In the x-direction, we have:

Force 2 + F4 * cos(theta) = 0.

Since the angle is not mentioned for F4, let's call it theta. Solving for F4, we get:

F4 = -Force 2 / cos(theta).

Now, in the y-direction, we have:

Force 1 * sin(52 degrees) + Force 3 + F4 * sin(theta) = 0.

Substituting the known values, we get:

46.0 * sin(52 degrees) + 34.5 + F4 * sin(theta) = 0.

Now we can solve for F4:

F4 * sin(theta) = -46.0 * sin(52 degrees) - 34.5.

F4 = (-46.0 * sin(52 degrees) - 34.5) / sin(theta).

But wait a minute, we don't know the value of theta, do we? Oh boy, this is turning into a circus act! Without more information, we can't find the exact magnitude of F4.

So, my friend, it seems like we're at a bit of a standstill. We'll need more information to solve for the magnitude of F4. Maybe next time we can bring our clown car and a few more tricks to the equation!

To find the magnitude of the last force, F4, we need to use the concept of static equilibrium. In static equilibrium, the net force and the net torque acting on an object are both zero.

To find the magnitude of the last force, F4, we'll break it down into its components using trigonometry. Let's consider the x-axis and y-axis separately.

Along the x-axis:
Force 1 has a component along the x-axis, which can be found by multiplying its magnitude (46.0 N) by the cosine of the angle it makes with the positive x-axis (52 degrees). So, the x-component of Force 1 is: F1x = 46.0 N * cos(52 degrees) = 29.6002 N.

Force 2 is already acting along the positive x-axis, so its x-component is simply equal to its magnitude: F2x = 29 N.

The x-component of the last force, F4x, must be equal in magnitude but opposite in direction to the sum of the x-components of Forces 1 and 2, in order for the net force along the x-axis to be zero. Therefore, F4x = -(F1x + F2x) = -(29.6002 N + 29 N) = -58.6002 N.

Along the y-axis:
Force 3 is acting along the negative y-axis, so its y-component is equal to its magnitude: F3y = 34.5 N.

The y-component of the last force, F4y, must be equal in magnitude but opposite in direction to the y-component of Force 3, in order for the net force along the y-axis to be zero. Therefore, F4y = -(F3y) = -(34.5 N) = -34.5 N.

Now, using these x- and y-components of the last force, F4, we can find its magnitude using the Pythagorean theorem. The magnitude of F4 can be calculated as follows:

|F4| = sqrt(F4x^2 + F4y^2)
= sqrt((-58.6002 N)^2 + (-34.5 N)^2)
= sqrt(3431.03004 N^2 + 1190.25 N^2)
= sqrt(4621.28004 N^2)
≈ 68.0 N (Rounded to 3 significant figures)

Therefore, the magnitude of the last force, F4, is approximately 68.0 N.