Rotational Equilibrium Question

In summary, the problem involves a bar of uniform density, length L, and mass m suspended by two ropes of tensions T1 and T2 at either extremity of the bar. The bar is tilted at an angle θ and a mass M is resting at a distance l from T1. Using the equations Tnet = 0 and Fnet = 0, we can set up two equations to find the value of l in units of L. By setting the pivot point at the end of the bar on the side of T1, we can write the net torque equation as Mg*l + mg*L/2 - Ft2sinθ*L = 0. Similarly, the net force equation can be written as Ftcosθ +
  • #1
Joshd99

Homework Statement


A bar of uniform density, length L, and mass m is suspended by two ropes of tensions T1 and T2 at either extremity of the bar. The bar is tilted such that it makes an angle θ with the ropes. A mass M is resting at a distance l from T1.
https://i.imgur.com/vLlAJbe.png

If m=17.7kg, M=12.4kg, the angle θ=24.9, and the magnitude T1 is twice as large as T2, what is the distance l in units of L?

Homework Equations


Tnet = 0
Fnet = 0

The Attempt at a Solution


I started off by setting the pivot point at the end of the bar on the side of T1, and therefore the net torque equation should become Mg*l + mg*L/2 - Ft2sinθ*L = 0.

Next I set the net force equation as Ftcosθ + 2*Ftcosθ - mg - Mg = 0

Unsure of how to solve the question as I'm stuck with 2 equations and 3 unknowns L l and Ft
 
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  • #2
What is Ft? Just write an expression for the vertical component of the net force and set it equal to zero.

On edit: You're not supposed to find L. The problem is asking you to find ##l## in units of L. That means finding ##l## as some number times L.
 
Last edited:
  • #3
kuruman said:
What is Ft? Just write an expression for the vertical component of the net force and set it equal to zero.

On edit: You're not supposed to find L. The problem is asking you to find ##l## in units of L. That means finding ##l## as some number times L.
thanks for the reply, figured it out with what you mentioned in the edit :)
 

FAQ: Rotational Equilibrium Question

1. What is rotational equilibrium?

Rotational equilibrium is a state in which an object is not experiencing any net torque, meaning that it is not rotating or accelerating in a rotational direction. This can occur when the sum of all the torques acting on an object is equal to zero.

2. What factors affect rotational equilibrium?

The factors that affect rotational equilibrium include the forces acting on the object, the distance of the forces from the pivot point, and the direction of the forces relative to the pivot point. The distribution of mass and the shape of the object also play a role in rotational equilibrium.

3. How do you calculate rotational equilibrium?

To calculate rotational equilibrium, you must first determine the sum of all the torques acting on the object. This can be done by multiplying the force by the distance from the pivot point. If the sum of the torques is equal to zero, the object is in rotational equilibrium. If not, the object will rotate in the direction of the larger torque.

4. What is the importance of rotational equilibrium in physics?

Rotational equilibrium is important in physics because it allows us to understand and predict the behavior of objects that are rotating or in rotational motion. It is also a fundamental principle in many areas of physics, such as mechanics and fluid dynamics.

5. How is rotational equilibrium different from translational equilibrium?

Rotational equilibrium refers to the state of an object when it is not rotating, while translational equilibrium refers to the state of an object when it is not moving in a linear direction. In rotational equilibrium, the net torque is zero, whereas in translational equilibrium, the net force is zero.

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