Rotational equilibrium problem

In summary: This means that you cannot combine them like you did in your equation. You have to use the perpendicular distance for each component separately. In summary, the conversation is about a problem where the final answer cannot be reached correctly. The forces are projected along the x and y axis, and the figure is in translational and rotational equilibrium. The net torque is zero, so the torque is calculated using the pivot point. However, there seems to be a mistake in the torque equation, as the book's answer is different from the calculated answer. It is suggested that the perpendicular distances for each component of F1 should be used separately in the equation.
  • #1
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http://img95.imageshack.us/img95/9403/problempi4.png [Broken]

I know this problem isn't hard, but I can't reach the final answer in the back.

OK, so if we project the forces along the x and y axis, we can easily conclude that:

F_(T,2) + F_(T,1) * sin50 = 10
F_(T,1) * cos50 = P

from here, though, I seem to be doing something wrong. The figure is in translational and rotational equilibrium, so net torque is zero. Let's take F_(T,2) as pivot. Then

F_(T,2)(0) + F_(T,1) * sin50(.30) = 10(.15)

Final answer will be

F_(T,1) = 6.59

where as the book's answer is 11. Of course I can't continue from here and find the other forces, so I'll just leave it at that.

Heh. Thanks all.
 
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  • #2
What happened to the F applied at P in your torque equation?
 
  • #3
It's along the x-axis, so it isn't calculated (it goes through the pivot).
 
  • #4
ianb said:
It's along the x-axis, so it isn't calculated (it goes through the pivot).

No, OlderDan is right, you are taking moment (torque) about a point!, not about an axis (which is defined differently).

Unless you meant about the left down corner, which in that case you forgot one of the F(t,1) components torque. Maybe you should be more clear.
 
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  • #5
Wow, okay, then I guess we could say

F_(T,2)(0) + F_(T,1) * sin50(.30) + F_(T,1) * cos50(.30) = 10(.15)

but that will give F_(T,1) = 3.55, which is incorrect. Of course, I could have made something wrong there but there is a catch somewhere that I probably wasn't taught before.
 
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  • #6
ianb said:
Wow, okay, then I guess we could say

F_(T,2)(0) + F_(T,1) * sin50(.30) + F_(T,1) * cos50(.30) = 10(.15)

but that will give F_(T,1) = 3.55, which is incorrect. Of course, I could have made something wrong there but there is a catch somewhere that I probably wasn't taught before.
If you use the lower left corner for the torque calculation, the two components of F1 produce torques in opposite directions and have different perpendicular distances.
 

1. What is rotational equilibrium?

Rotational equilibrium refers to the state where an object is not rotating or accelerating around its center of mass. This means that the sum of all the clockwise torques acting on the object is equal to the sum of all the counterclockwise torques, resulting in a net torque of zero.

2. How is rotational equilibrium different from static equilibrium?

Rotational equilibrium only considers the balance of torques acting on an object, while static equilibrium considers both the balance of forces and torques. In other words, an object can be in rotational equilibrium but not in static equilibrium if there is a net force acting on it.

3. What is the purpose of solving a rotational equilibrium problem?

The purpose of solving a rotational equilibrium problem is to determine the unknown variables, such as the force or torque acting on an object, in order to understand the motion or stability of the object. This is important in various fields, such as engineering, physics, and biomechanics.

4. What are some real-life examples of rotational equilibrium?

Some examples of rotational equilibrium in real life include a balanced see-saw, a spinning top, a bicycle wheel rolling without wobbling, and a spinning figure skater maintaining a certain position. In each of these cases, the sum of all the torques acting on the object is equal to zero.

5. How do you solve a rotational equilibrium problem?

To solve a rotational equilibrium problem, you need to identify the unknown variables, draw a free-body diagram of the object, and apply the rotational equilibrium equation (Στ = 0). This equation states that the sum of all the torques acting on an object is equal to zero. Then, you can use algebraic methods to solve for the unknown variables.

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