Statics/Equilibrium Physics question-- Two weights and a single pulley

In summary, the problem involves a 60 lb weight (A) connected to a 65 lb weight (C) by a rope that goes over a pulley at point B. The horizontal distance between A and B is 15 in and the height between A and B is represented by h. The goal is to determine the value of h and the horizontal force acting on A in order for the system to be in equilibrium. Using the equations ∑Fx = 0 and ∑Fy = 0, it can be determined that the total tension in the rope is equal to TBA = TBAy x sin(tan-1(h/15 in.)) and TBA = TBAx x cos(tan-1
  • #1
zubb999
2
0

Homework Statement


The 60 lb collar "A" is on a friction-less vertical rod and is connect to a 65 lb counterweight "C". Determine the value "h" (which is the height between "A" and "B") for which the system is in equilibrium. Also, find the horizontal force "N" acting on collar "A".
Here is a rough typed up picture of what the picture looks like, the zeros (0) are empty space

<--15in-->
00000000B0 ^
0000000/0|0 |
000000/00|0 |
00000/000|0 |
0000/000 C0 h
000/0000000 |
00/00000000 |
0/000000000 |
A0000000000v

The horizontal distance between A and B is 15 in. There is a pulley at B and a rope/string going from a A to B, and B to C. From what I can tell, the rope is continuous from points A to C. I have no idea where to get started on this or how to ultimately find h or the horizontal force acting on point A.
A is a 60 lb weight.
C is a 65 lb weight.

Homework Equations


All I have so far are these few things:
∑Fx = 0
∑Fy = 0
TBC = 65 lb
TBA = 65 lb

The Attempt at a Solution


I really don't know where to begin with this problem. I'm thoroughly confused as to how I should go about finding "h" or the horizontal force at "A", and I haven't been able to find similar problems to this one. If anyone can help me out, it'd be much appreciated.
 
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  • #2
Hello Zubb, and welcome to PF.

Nice picture.. :smile:
As a first step it might be nice to consider only A and the section AB of the rope. What vertical force is needed to keep A from moving up (or down) ?
The rope can only exercise a force in a direction along the rope. With one component known and the tangent of the angle expressed in h and the 15 in, you have an expression for the total tension in the rope. Then it's time to bring B and C back in the considerations.
 
  • #3
Ok...

So according to what you just said, I should have this at my disposal:
TBAy = 60 lb.
tanθ = h/15 in. --> θ=tan-1(h/15 in.)
If TBA = TBAy x sinθ
then TBA = TBAy x sin(tan-1(h/15 in.))
If TBA = TBAx x cosθ
then TBA = TBAx x cos(tan-1(h/15 in.))

Right?

And then when I bring TBC to put all this into the ∑Fx and ∑Fy equations, and I end up with this:
∑Fx = TBA/(cos(tan-1(h/15 in.))) = 0? [substituted TBAx out]
∑Fy = A[-60 lb.] + C[-65 lb.] + TBA/(sin(tan-1(h/15 in.))) + TBC[65 lb.] = 0 [substituted TBAy out]

I'm terribly sorry, but I'm not seeing how this helps me... :cry:
I really do appreciate this help though. :biggrin:
 
  • #4
Well, you have TBA,y, you have TBA and you have a relationship with one unknown, h.
What can be easier ? :smile:
 
  • #5


I would approach this problem by first drawing a free body diagram to visualize all the forces acting on the system. From the given information, we know that there are two weights, 60 lb and 65 lb, connected by a rope passing over a single pulley at point B. The rope is continuous from points A to C, so we can assume that the tension in the rope is the same at all points.

Next, I would apply the principles of statics and equilibrium to the system. This means that the sum of all the forces in the x-direction and the y-direction must equal zero. We can write this mathematically as ∑Fx = 0 and ∑Fy = 0.

For the x-direction, we have the horizontal force acting on A, which we can label as N, and the tension in the rope, which we can label as TBA. Since there are no other forces acting in the x-direction, we can write ∑Fx = N - TBA = 0.

For the y-direction, we have the weight of collar A, which we can label as W, and the tension in the rope, which we can label as TBA. We also have the weight of counterweight C, which we can label as Wc. Again, since there are no other forces acting in the y-direction, we can write ∑Fy = W + Wc - TBA = 0.

Since we have two equations and two unknowns (N and TBA), we can solve for both of them. Once we have the values for N and TBA, we can use trigonometry to find the height h, which is the distance between points A and B.

To find the horizontal force at A, we can simply substitute the value of TBA into the equation for N. This will give us the value for N in terms of known quantities.

In summary, to solve this problem, I would first draw a free body diagram and then apply the principles of statics and equilibrium to write equations for the x-direction and y-direction. From there, I would solve for the unknowns, N and TBA, and then use trigonometry to find the height h. Finally, I would use the value of TBA to find the horizontal force at A.
 

FAQ: Statics/Equilibrium Physics question-- Two weights and a single pulley

What is statics/equilibrium physics?

Statics/equilibrium physics is a branch of physics that deals with the analysis of objects at rest or in a state of constant motion. It involves the study of forces and their effects on objects, as well as how objects maintain balance and stability.

What is the purpose of using a single pulley in a physics problem?

A single pulley is often used in physics problems to change the direction of a force or to reduce the amount of force needed to lift an object. It can also be used to transfer forces from one object to another.

How do you calculate the tension in a rope or string connected to a single pulley?

The tension in a rope or string connected to a single pulley can be calculated using the equation T = (m1 * g) / (2 * sinθ), where T is the tension, m1 is the mass of the object being lifted, g is the acceleration due to gravity, and θ is the angle of the rope or string with respect to the horizontal.

What is the difference between static equilibrium and dynamic equilibrium?

Static equilibrium refers to a state in which an object is at rest or moving at a constant velocity with no net force acting on it. Dynamic equilibrium, on the other hand, refers to a state in which an object is moving at a constant velocity with balanced forces acting on it. In other words, static equilibrium involves no motion, while dynamic equilibrium involves constant motion.

How can you determine if an object is in equilibrium using a free body diagram?

To determine if an object is in equilibrium using a free body diagram, you must first draw a diagram of the object showing all the external forces acting on it. Then, using the equations of equilibrium, you can calculate the net force in each direction. If the net force is zero, the object is in equilibrium. If the net force is not zero, the object is not in equilibrium and will either accelerate or continue moving at a constant velocity.

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