Another Doubt From Halliday Resnick Krane -- Puck on a string in circular motion

In summary, a puck with constant speed v0 is moving in a circle of radius r0 on a frictionless table, held in place by a string attached to a hanging mass M. The tension in the string caused by the weight of M acts as the centripetal force for the circular motion. An initial push is required to start the motion, and in the absence of friction, a steady state can be achieved.
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vibha_ganji
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Hello! This is a problem from Halliday Resnick Krane (Chapter 4: Problem #15). “A puck is moving in a circle of radius r0 with a constant speed v0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is attached on the other end to a hanging object of mass M.” What I don’t understand is how this system works. How does hanging a heavy mass through a table make the mass m on the table spin in a circle?
 
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  • #2
Someone has given it an initial push sideways to make it circle as described. After a small time, absent friction, a steady state can ensue.
 
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  • #3
The weight of the mass M causes tension in the string. The tension then acts as the centripetal force required for circular motion. As @hutchphd mentioned an initial push is required to start the circular motion.
 

1. What is the setup of the "Puck on a string in circular motion" problem?

The problem involves a puck attached to a string and moving in a circular motion with a constant speed. The string is attached to a fixed point and the puck is moving in a horizontal plane.

2. How do you find the tension in the string in this problem?

The tension in the string can be found using the centripetal force equation: T = mv²/r, where T is the tension, m is the mass of the puck, v is its velocity, and r is the radius of the circular motion.

3. What is the relationship between the speed of the puck and the radius of the circular motion?

The speed of the puck is directly proportional to the radius of the circular motion. This means that as the radius increases, the speed also increases, and vice versa.

4. How does the direction of the velocity of the puck change as it moves in a circular motion?

The direction of the velocity of the puck is constantly changing as it moves in a circular motion. This is because the velocity is always tangent to the circular path and therefore, it changes direction as the puck moves along the path.

5. How does the mass of the puck affect its motion in this problem?

The mass of the puck does not affect its motion in this problem, as long as the speed and radius of the circular motion remain constant. This is because the mass cancels out in the centripetal force equation, and only the speed and radius have an effect on the tension in the string and the motion of the puck.

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