Stone tied to string whirled. Max string tension?

• itwazntme
In summary, the question is asking at what point the tension in the string will be maximum as a stone of mass m is whirled in a vertical circle at a constant speed. The answer is at the bottom of the circle, where the force required to overcome the effect of gravity is greatest. This can be proven mathematically by analyzing the forces acting on the stone at different points and applying Newton's 2nd law, taking into account the acceleration of the stone at each point.
itwazntme
stone tied to string whirled. Max string tension??

Homework Statement

A stone of mass m at the end of a string of length l is whirled in a vertical circle at a constant speed when will the tension in the string be maximum?

Homework Equations

a) at the top of the circle
b) halfway down from the top
c) quarterway down from the top
d) at the bottom of the circle

The Attempt at a Solution

i know the answer, its obvious its the bottom of the circle due to force required to overcome the effect of gravity, but how can one prove it mathematically using the different physics phenomenon.

Analyze the forces acting on the stone at each of those points, then apply Newton's 2nd law. Hint: What's the acceleration of the stone at each point?

I would approach this problem by using the equation for centripetal force, F=mv^2/r, where m is the mass of the stone, v is the velocity, and r is the radius of the circle.

At the top of the circle, the tension in the string would be equal to the weight of the stone, mg. This is because at the top of the circle, the centripetal force is equal to the weight of the stone, since there is no other force acting on the stone in the vertical direction.

Halfway down from the top, the tension in the string would be less than the weight of the stone, but greater than at the top. This is because at this point, the centripetal force is equal to the weight of the stone minus the tension in the string, which is acting in the opposite direction of the weight.

At a quarter of the way down from the top, the tension in the string would be even less, as the centripetal force is now equal to the weight of the stone minus the tension in the string, minus the weight of the stone again. This is because at this point, the weight of the stone is acting in the same direction as the tension in the string.

Finally, at the bottom of the circle, the tension in the string would be at its maximum. This is because at this point, the centripetal force is equal to the weight of the stone plus the tension in the string, as the weight of the stone is now acting in the opposite direction of the tension in the string.

Therefore, mathematically, we can prove that the tension in the string will be maximum at the bottom of the circle, as it is the point where the centripetal force is equal to the weight of the stone plus the tension in the string.

1. What is the purpose of tying a stone to a string and whirling it?

The purpose of this experiment is to demonstrate the concept of centripetal force. When the string is whirled, the stone moves in a circular motion due to the tension in the string pulling it towards the center.

2. How does the length of the string affect the maximum tension it can withstand?

The longer the string, the greater the distance the stone must travel in a circular motion. This requires a higher tension in the string to keep the stone moving in a circular path. Therefore, longer strings can withstand higher maximum tension.

3. Is there a limit to the maximum tension that the string can withstand?

Yes, there is a limit to the maximum tension that the string can withstand. This limit is determined by the material and thickness of the string. If the tension exceeds this limit, the string will break.

4. What happens if the string is not strong enough to withstand the maximum tension?

If the string is not strong enough, it will break and the stone will fly off in a straight line tangent to its circular path. This is due to the principle of inertia, where an object in motion will continue to move in a straight line unless acted upon by an external force.

5. Can the maximum tension of the string be increased by increasing the speed of whirling?

Yes, the maximum tension of the string can be increased by increasing the speed of whirling. This is because the centripetal force, and therefore the tension in the string, is directly proportional to the square of the speed of whirling.

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