Vectors, Components and some Horizontal Force?

[TheLastLaw]

Homework Statement

A mass of 100kg is suspended by two ropes that make angles of 60° to the horizontal. If a horizontal pull of 200N, in a plane perpendicular to the plane of the other forces is applied find the tension in the ropes after equilibrium has occurred.

m=60kg
Fg=mg=(60kg)(9.8N/kg)
Fh=200N

Answer is supposed to be: T1=T2=577N
θ=11.5° to vertical for Fh

T1 and T2 can be solved for using vectors but I really don't know how to make use of them.

Homework Equations

The use of the cosine and sine law as well as trig ratios and components. Some of the components would be T1h (horizontal), T1v (vertical), T2h and T2v.

The Attempt at a Solution

I really don't know how to incorporate the vertical force into the solution or WHERE it is for that matter and what is meant by "after equilibrium." Using the info, I know that the triangle that is formed has three 60° angles and is equilateral herewith. I can find the components and use Newton's first law to state:

1. T2 cos 60 = T1 cos 60
2. T2 sin 60 + T1 sin 60 = Fg

Using substitution, I found that T1=T2= 565.8N but this is STILL the solution without this "horizontal force" and thsu incorrect. I think that equilibrium occurs when the horizontal force is equal in both directions and thus is 0N but if that's the case, why is 200N required?

Thank you so much for any help that is given! ^^

 

[anathema]

To solve this problem, you will need to use the concept of vector addition. First, draw a diagram of the situation with all the forces acting on the mass. This will help you visualize the problem and determine the direction and magnitude of each force.

Next, use the equations you listed in the "Homework Equations" section to set up a system of equations. You will have three unknowns: T1, T2, and θ (the angle between the vertical and Fh). Use the fact that the sum of the forces in the horizontal and vertical directions must equal zero at equilibrium to set up your equations.

For example, in the horizontal direction, you will have:

T1cos60 + T2cos60 + Fh = 0

And in the vertical direction, you will have:

T1sin60 + T2sin60 + Fg = 0

Solving these equations for T1 and T2 will give you the correct values for the tensions in the ropes. You can then use the trigonometric functions to solve for θ.

Remember to pay attention to the direction of the forces and use vector addition to find the resultant force. Good luck!

 

[Moetasim]

I would approach this problem by first understanding the physical principles involved, and then using mathematical equations to solve for the unknown values.

In this scenario, the mass is suspended by two ropes, which means that there are two forces acting on the mass: the weight of the mass (Fg) and the tension in the ropes (T1 and T2). The horizontal force (Fh) is a third force that is applied perpendicular to the other two forces.

To find the tension in the ropes after equilibrium has occurred, we need to use the concept of equilibrium. This means that all forces acting on the mass must balance out, resulting in a net force of 0N. In other words, the mass is not moving or accelerating in any direction.

To solve for the unknown values, we can use the equations of equilibrium:

ΣFh = 0
ΣFv = 0

In this case, ΣFh = T1h + T2h + Fh = 0 (since Fh is applied horizontally)
and ΣFv = T1v + T2v - Fg = 0 (since Fg is acting downwards)

We can also use trigonometric ratios to relate the horizontal and vertical components of the tension in the ropes to the angles and forces involved. For example, T1h = T1 cos 60° and T1v = T1 sin 60°.

Solving these equations simultaneously, we can find that T1 = T2 = 577N and θ = 11.5° to the vertical for the horizontal force.

To incorporate the horizontal force into the solution, we must consider the fact that this force is acting perpendicular to the other forces. This means that it is not directly affecting the vertical components of the tension in the ropes, but rather contributing to the horizontal components. By including this force in our equations of equilibrium, we can solve for the unknown values and find the correct solution.

In conclusion, as a scientist, I would use my understanding of physical principles and mathematical equations to approach this problem and find the correct solution.