Solving for Tension in Rope

In summary, the problem involves a 24 kg beam leaning against a smooth wall, held in place by a horizontal rope on a frictionless floor. The beam makes an angle of 55 degrees with the floor. The equations used involve torque, force, and distance, and the conditions for equilibrium include both net torque and net force being equal to zero. The forces acting on the beam must be identified, including their direction and symbol.
  • #1
Fusilli_Jerry89
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Homework Statement


A 24 kg beam of length 2.4 m leans against a smooth wall. A horizontal rope is tied to the wall and holds the beam on a frictionless floor. The beam makes an angle of 55 degrees with the floor. WHat is the tension in the rope? (The rope is on the floor.


Homework Equations


torque=force|| x distance


The Attempt at a Solution


(Torque at the bottom of the beam)
24kg x 9.8 x cos55 x 1.2m + T x cos35 x 2.4m = F(normal1) x cos55 x 2.4m

(torque at the top)
24kg x 9.8 x cos55 x 1.2m = F(normal2) x cos35 x 2.4m + Ff x cos55 x 2.4m

Now what?
 
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  • #2
I don't understand your equations. Please identify all the forces acting on the beam: where they act, their direction and symbol.

Also realize that setting net torque equal to zero is only one of the conditions for equilibrium. What about the net force?
 
Last edited:
  • #3


I would approach this problem by first identifying the known values and variables, and then using the relevant equations and principles to solve for the unknown quantity, which in this case is the tension in the rope. From the given information, we know that the beam has a mass of 24 kg and a length of 2.4 m, and it is making an angle of 55 degrees with the floor. We also know that the rope is tied to the wall and is holding the beam on a frictionless floor.

To solve for the tension in the rope, we can use the principle of equilibrium, which states that the sum of all the forces acting on an object must be equal to zero. In this case, the forces acting on the beam are its weight, the normal forces from the wall and floor, and the tension in the rope. We can set up two equations, one for the vertical forces and one for the horizontal forces, and solve for the tension.

For the vertical forces, the sum of the forces in the y-direction must be equal to zero, since the beam is not moving up or down. This means that the weight of the beam must be balanced by the normal forces from the wall and floor. We can write this as:

F(normal1) + F(normal2) - 24kg x 9.8m/s^2 = 0

Solving for the normal forces, we get:

F(normal1) + F(normal2) = 235.2 N

For the horizontal forces, the sum of the forces in the x-direction must also be equal to zero, since the beam is not moving horizontally. This means that the tension in the rope must be balanced by the horizontal component of the weight of the beam. We can write this as:

T - 24kg x 9.8m/s^2 x sin55 = 0

Solving for the tension, we get:

T = 163.5 N

Therefore, the tension in the rope is 163.5 N. This means that the rope is pulling on the beam with a force of 163.5 N, which is equal and opposite to the horizontal component of the weight of the beam.

In conclusion, by using the principle of equilibrium and applying relevant equations, we can solve for the tension in the rope and understand the forces acting on the beam in this scenario.
 

1. What is tension in a rope?

Tension in a rope is the force that is exerted on the rope when it is pulled taut. It is the reaction force that opposes the pulling force applied to the rope.

2. How is tension calculated in a rope?

Tension can be calculated using the formula T = F * L, where T is the tension in the rope, F is the force applied to the rope, and L is the length of the rope. This formula assumes the rope is in equilibrium.

3. What factors affect tension in a rope?

The factors that affect tension in a rope include the weight of the object being lifted, the angle of the rope, and any external forces acting on the rope, such as wind or friction.

4. How can tension in a rope be increased?

Tension in a rope can be increased by increasing the force applied to the rope or by decreasing the length of the rope. For example, pulling harder on the rope or using a shorter rope will increase tension.

5. How can tension in a rope be decreased?

Tension in a rope can be decreased by decreasing the force applied to the rope or by increasing the length of the rope. For example, pulling less on the rope or using a longer rope will decrease tension.

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