Forces in Two Dimensions - Mission F2D4 Detailed Help

A sign with a mass of m is hung symmetrically from two cables that make an angle of theta with the horizontal (see diagram). The tension in each one of the cables is F_tens. The vertical component of the tension force is F_y; the horizontal component is F_x. Which of the following mathematical statements are true?

Definition of Equilibrium:
Equilibrium is the condition in which all the individual forces acting upon an object are balanced.

If an object is at equilibrium, then the individual forces acting upon the object are balanced. There is no unbalanced force - the net force is 0 Newton. All the vertical forces balance and all the horizontal forces balance.

In this situation, there are two forces that are at angles to the vertical and horizontal (the tension forces). It is the usual strategy to first resolve any force at angles to the axis into components or parts that are directed along the axis. Thus, each tension force has a horizontal component (F_x) and a vertical component (F_y). The two vertical components are directed upward and together they must balance the downward force of gravity. The two horizontal components are directed left and right and must balance each other.

The tension force has a horizontal and an upward component or effect on the sign. The horizontal component (F_x) can be calculated as F_tens• cosine(Θ) where Θ is the angle that the force makes with the horizontal. The upward component (F_y) can be calculated as F_tens• sine(Θ) where Θ is the angle that the force makes with the horizontal.

F_x= F_tens• cosine(Θ)

F_y= F_tens• sine(Θ)

The force of gravity (F_grav) acting upon an object can be determined from the mass of an object using the equation:

F_grav= mass • g

where g is the acceleration caused by gravity alone. The value of g on Earth is 9.8 m/s/s.

Tired of Ads?
Go ad-free for 1 year