Calculating Tension in a Moving String: Is it Possible?

In summary, the conversation discusses the relationship between tension in a string holding up a hanging mass and the forces acting on the objects connected by the string. The tension is equal to the product of the mass and gravity, but must be less than the weight of the hanging mass in order for it to move. The conversation also explores the use of Newton's 2nd law to calculate the tension and acceleration of the objects.
  • #1
MrLobster
6
0
I understand that if a string is holding up a hanging mass then the magnitude of the tension in the string is mass * gravity.

The other end of the string is tied to an object on a flat surface (after being redirected by a frictionless pully). If the tension force is great enough to overcome static friction then the object, string, and mass will move. If I know all the relevant weights and coefficients of friction is there a way to calculate the magnitude of the tension in the string?

It must be less than mass * gravity because the mass is being pulled down.
It can't be the same as the frictional force slowing the object because the object is moving too.
 
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  • #2
MrLobster said:
I understand that if a string is holding up a hanging mass then the magnitude of the tension in the string is mass * gravity.
If the hanging mass is in equilibrium, then you are correct.

The other end of the string is tied to an object on a flat surface (after being redirected by a frictionless pully). If the tension force is great enough to overcome static friction then the object, string, and mass will move. If I know all the relevant weights and coefficients of friction is there a way to calculate the magnitude of the tension in the string?
Sure. Apply Newton's 2nd law to both masses.

It must be less than mass * gravity because the mass is being pulled down.
If the hanging mass is accelerating, then you are correct: the upward force of the string must be less than the weight of the mass.
It can't be the same as the frictional force slowing the object because the object is moving too.
Again, if the system is accelerating you are correct. There must be a net force on each accelerating mass.
 
  • #3
Doc Al said:
Sure. Apply Newton's 2nd law to both masses.

Do I need to know the tension in the string or the accelerations of the objects to do this? I was going to use the tension of the string to figure out the accelerations on the objects which should be equal since they are connected by a string.

Hmmm. Can you verify if I'm on the right track if I say:

The magnitude of the force on the mass: mass * gravity - magnitude of the frictional force on the object?

The accelerations for *both* the object and mass would be the force on the mass / mass?

Then I can calculate the force on the object and tension in the rope based on that start...
 
  • #4
MrLobster said:
Do I need to know the tension in the string or the accelerations of the objects to do this? I was going to use the tension of the string to figure out the accelerations on the objects which should be equal since they are connected by a string.
Generally the tension and the acceleration is what you are trying to find. By setting up Newton's 2nd law for the object and the hanging mass you'll get two equations with two unknowns: the tension and the acceleration.

Hmmm. Can you verify if I'm on the right track if I say:

The magnitude of the force on the mass: mass * gravity - magnitude of the frictional force on the object?
No. The net force on the hanging mass is mg (downward) - tension force (upward). (Don't take shortcuts.)

The accelerations for *both* the object and mass would be the force on the mass / mass?
The acceleration of any mass equals the net force on it divided by its mass. This is just Newton's 2nd law and its the key to solving these kinds of problems.

Do this. Identify all the forces acting on each mass. Then write down Newton's 2nd law for each mass:
[tex]\vec{F}_{net} = \Sigma \vec{F} = m \vec{a}[/tex]

If you do it right, you'll get two equations with two unknowns. Solve!
 
  • #5
Thank you, this problem is clear to me now.
 

1. What is tension in a moving string?

Tension in a moving string refers to the force that is transmitted through the string when it is pulled or stretched. It is the force that keeps the string taut and allows it to vibrate when in motion.

2. How is tension affected by the speed of the string?

The tension in a moving string is directly proportional to the speed of the string. This means that as the speed of the string increases, so does the tension. This is because the faster the string moves, the stronger the force that is required to keep it taut.

3. What factors affect the tension in a moving string?

There are several factors that can affect the tension in a moving string. These include the length and thickness of the string, the material it is made of, and the amount of force applied to it. Additionally, the speed and direction of the string's movement can also impact the tension.

4. How does tension affect the pitch of a string instrument?

Tension plays a crucial role in determining the pitch of a string instrument. As the tension in a string increases, the frequency of its vibrations also increases, resulting in a higher pitch. Similarly, decreasing the tension lowers the pitch of the string.

5. Can tension in a moving string be measured?

Yes, tension in a moving string can be measured using a device called a tension meter. This instrument measures the amount of force being applied to the string and provides a numerical value for the tension. This is important for musicians and engineers who need to ensure that the string is at the right tension for optimal performance.

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