What is the Magnitude of the Third Force in a Three-Force System?

[purplecows]

Homework Statement

An object that is moving at a constant speed velocity is acted upon by three forces. One force is 150 N along the x-axis, the second is 100 N along a direction making a counterclockwise angle of 120° with the x-axis. What is the magnitude of the third force?

Homework Equations

Not sure, these are the only ones I THINK are remotely relevant (but I have no idea which is why I'm posting here)

F_x = Fcosθ
F_y = Fsinθ

The Attempt at a Solution

I thought it would just be either 100 N (the same as the northwest force 120° from x-axis) or it would be something involving the Pythagorean Theorem (100^2 + f^2 = 150^2 or 100^2 + 150^2 = 150^2)


Anyone? This is urgent. My whole class is confused.

 

[Pythagorean]

Since it's moving at a constant velocity, what is the sum of the forces on the object?

 

[purplecows]

Since it's moving at a constant velocity, what is the sum of the forces on the object?

zero

 

[Pythagorean]

And the x and y directions are independent. So you have two equations, two variables, yeah?

 

[Nickie]

I would approach this problem by first identifying the forces acting on the object and their respective directions. In this case, we have a force of 150 N along the x-axis, and a force of 100 N at an angle of 120° from the x-axis. The third force is unknown, but we can assume it is acting in a different direction than the first two forces.

Next, I would use vector addition to find the resultant force acting on the object. This can be done by breaking down the forces into their x and y components using the equations Fx = Fcosθ and Fy = Fsinθ. In this case, the x-component of the first force is 150 N, and the y-component of the second force is 100 N. The x-component of the second force can be found using the angle given (120°) and the Pythagorean theorem.

Once we have the x and y components of the resultant force, we can use vector addition to find the magnitude and direction of the third force. This can be done using the equation F = √(Fx^2 + Fy^2) and the inverse tangent function to find the direction of the force.

In summary, the magnitude of the third force can be found using vector addition and trigonometric functions. It is important to note that the direction of the third force will depend on the specific values given for the first two forces.