How Do You Calculate the Second Mass in a Static Equilibrium Problem?

In summary, the conversation discusses a scenario in which a 0.105 kg meter stick is supported by a string attached to the ceiling, with a 0.665 kg object hanging vertically and a second mass attached to keep it in equilibrium. The question asks to find the value of the second mass when the tension in the string is given as 21.2 N. Using the equations for the acceleration of gravity and sum of forces and torques, a solution of 1.47786 kg is obtained, but the mass of the stick was initially left out. Upon considering the mass of the stick, the correct solution is found.
  • #1
jfri14
3
0

Homework Statement


A 0.105 kg meter stick is supported at its
40 cm mark by a string attached to the ceiling.
A 0.665 kg object hangs vertically from the
7.17 cm mark. A second mass is attached
at another mark to keep it horizontal and in
rotational and translational equilibrium.

If the tension in the string attached to the
ceiling is 21.2 N, find the value of the second
mass. Answer in units of kg.


Homework Equations


The acceleration of gravity is 9.8 m/s2
Sum of Forces= 0
Sum of Torques =0


The Attempt at a Solution



Since the sum of the forces =0
21.2N - 0.665kg*9.8m/s2 - x*9.8m/s2 = 0
1.47786 kg

I'm not sure why this isn't right or how to fix it
 
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  • #2
jfri14 said:

The Attempt at a Solution



Since the sum of the forces =0
21.2N - 0.665kg*9.8m/s2 - x*9.8m/s2 = 0
1.47786 kg
You left out the mass of the stick itself.
 
  • #3
Got it, thanks so much!
 

FAQ: How Do You Calculate the Second Mass in a Static Equilibrium Problem?

What is a static equilibrium problem?

A static equilibrium problem refers to a situation where an object is at rest and all the forces acting on it are balanced, resulting in no net movement. This means that the object remains in a constant position without any acceleration.

How do you solve a static equilibrium problem?

To solve a static equilibrium problem, you need to first identify all the forces acting on the object and their directions. Then, you can use the equations of equilibrium - sum of forces in the x-direction and sum of forces in the y-direction - to find the unknown forces and ensure that the object is in a state of equilibrium.

What are the key principles of static equilibrium?

The key principles of static equilibrium are the first and second conditions of equilibrium. The first condition states that the sum of all forces acting on an object must be equal to zero for the object to be at rest. The second condition states that the sum of all torques acting on an object must also be equal to zero for the object to be in rotational equilibrium.

What are some common examples of static equilibrium in everyday life?

Some common examples of static equilibrium in everyday life include a book resting on a table, a pencil standing upright on its tip, a shelf attached to a wall, and a seesaw with two people of equal weight on either end.

What are the applications of understanding static equilibrium?

Understanding static equilibrium is essential in various fields such as engineering, physics, and architecture. It is used to analyze and design structures, determine the stability of objects, and calculate the forces acting on different parts of a system. It is also crucial in understanding the mechanics of everyday objects and how they maintain their balance.

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