A mass whirled in a horizontal plane

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SUMMARY

A mass tied to a string and whirled in a horizontal plane experiences tension that provides the necessary centripetal force for circular motion. The string cannot be perfectly horizontal; if it were, there would be no upward force to balance the downward gravitational force (mg). Instead, the string must make an angle with the vertical, creating a conical shape where the tension (T) is resolved into vertical (T*cos(x)) and horizontal (T*sin(x)) components. Thus, while the mass can travel in a horizontal plane, the string itself cannot remain horizontal.

PREREQUISITES
  • Understanding of centripetal force and its role in circular motion
  • Knowledge of tension in strings and its components
  • Familiarity with gravitational force (mg) and its implications
  • Basic principles of conical motion and angles
NEXT STEPS
  • Explore the concept of conical pendulums and their dynamics
  • Study the mathematical derivation of forces in circular motion
  • Learn about the effects of string tension on motion in physics
  • Investigate real-world applications of centripetal force in engineering
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Physics students, educators, and anyone interested in understanding the dynamics of circular motion and the forces involved in whirling objects.

Vijay Bhatnagar
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A mass is tied to a string and whirled in a horizontal plane. The tension in the string provides the centripetal force required for circular motion of the mass. But which force balances the weight mg of the mass?
 
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Is the string perfectly horizontal?
 
Yes, the string is perfectly horizontal. If it were not so, the vertical component of the tension would support the weight and the horizontal component provide the necessary centripetal force. However, when the string is horizontal there is no vertical component of the tension. As a result the mass will tend to fall down. Then, do we conclude that it is not possible to whirl the mass in a perfectly horizontal plane? But practically it does look possible to do so.
 
Realize that just because the mass travels in a perfectly horizontal plane, that doesn't mean that the string is horizontal. (In fact, it can't be!)
 
Get a friend to whirl an object around on a string over his head, and watch carefully. Start with the object orbiting rather slowly, then faster and faster. Does the string ever become perfectly horizontal?
 
Doc Al said:
Realize that just because the mass travels in a perfectly horizontal plane, that doesn't mean that the string is horizontal. (In fact, it can't be!)
It should not even be possible that the mass travels in a horizontal plane. It has a force mg downwards but no upward mg force.
 
lugita15 said:
It should not even be possible that the mass travels in a horizontal plane. It has a force mg downwards but no upward mg force.
It's easy to get the mass to travel in a horizontal plane. But the string can't be perfectly horizontal; if it were, there'd be no balancing upward force on the mass. (Perhaps you're saying the same thing?)
 
lugita15 said:
It should not even be possible that the mass travels in a horizontal plane. It has a force mg downwards but no upward mg force.
The upward force comes from the tension in the string.
 
Doc Al said:
It's easy to get the mass to travel in a horizontal plane. But the string can't be perfectly horizontal; if it were, there'd be no balancing upward force on the mass. (Perhaps you're saying the same thing?)
Yes, I am saying the same thing.
 
  • #10
Suppose you have a massless string and a mass m tied in the middle, then would you able to stretch the string perfectly straight by pulling it from both sides? No, that would take infinite force, because there's no verically upward force to balance the weight mg. In real life, that's why wires and cables sag down in the middle.

Similarly, the whirling string has to make an angle, say 'x', with the vertical in the downward direction. It lies on a cone, whose semi-vertical angle is 'x'. If 'T' is the tension in the string, then mg=T*cos(x). The centipetal force is T*sin(x). The mass m travels in a horizontal plane, but not the string.
 

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