Ratio of Lengths b/a for Torques Equilibrium

  • Thread starter gcombina
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In summary, the question asks for the ratio of lengths between a 3.0-kg ball and a 1.0-kg ball placed at opposite ends of a massless beam in equilibrium. The options for the ratio are 2.0, 2.5, 3.0, 4.0, and 5.0. To solve this, we can use the equation Σtorques = 0 and calculate the torques on each ball, keeping in mind the clockwise and anticlockwise senses. The answer cannot be determined without more information.
  • #1
gcombina
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3

Homework Statement


A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the ratio of the lengths, b/a?

(a) 2.0 (c) 3.0 (e) 5.0

(b) 2.5 (d) 4.0

Homework Equations

The Attempt at a Solution


so I did the Σtorques = 0 since the whole system is in equilibrium

Torque = Fl

1st Torque is
(mga)(level arm of a)

2nd Torque is

mgb(level arm of b)

3rd Torque is
I don't know
 
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  • #2
No figure was attached.

Why do you think that three torques are involved in this problem?
 
  • #3
When calculating torques you need to keep track of which sense applies to each. Usual is to pick one sense, anticlockwise say, as positive, then any clockwise torque will be negative. (There must be some of each for the total to be zero!)
 

Related to Ratio of Lengths b/a for Torques Equilibrium

1. What is the formula for calculating the ratio of lengths b/a for torques equilibrium?

The formula for calculating the ratio of lengths b/a for torques equilibrium is b/a = F1d1/F2d2, where b is the length of the second force, a is the length of the first force, F1 and F2 are the magnitudes of the forces, and d1 and d2 are the distances from the pivot point to each force.

2. How is the ratio of lengths b/a related to torques equilibrium?

The ratio of lengths b/a is a crucial factor in determining whether an object will be in torques equilibrium. If the ratio is equal to 1, the object will be in equilibrium, meaning that the clockwise and counterclockwise torques are balanced. If the ratio is greater than 1, the object will rotate in a clockwise direction, and if it is less than 1, the object will rotate in a counterclockwise direction.

3. What is the significance of the ratio of lengths b/a in terms of stability?

The ratio of lengths b/a also plays a role in determining the stability of an object. If the ratio is close to 1, the object will be more stable, as any slight disturbance will result in a smaller torque and therefore a smaller rotation. However, if the ratio is significantly greater or less than 1, the object will be less stable and more likely to tip over.

4. Can the ratio of lengths b/a be negative?

No, the ratio of lengths b/a cannot be negative. This is because both b and a, as well as F1 and F2, must be positive values in order for the formula to accurately represent the torques equilibrium. A negative value would indicate that the force is acting in the opposite direction, which would not be possible in this scenario.

5. How can the ratio of lengths b/a be used in practical applications?

The ratio of lengths b/a is commonly used in engineering and physics to design and analyze structures and objects. It can help determine the ideal placement of forces and the required lengths for stability and equilibrium. This ratio is also important in the design of simple machines, such as levers and seesaws.

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