Question

Consider if you were to vary the number of washers suspended on the end of the string, how would this affect the centripetal force? How would increasing the number of washers at the end of the string affect the periodic time of moving mass? Generally, explain the effect of moving mass and radius on centripetal force.

Please give explantations

Answer 1

If we increase the number of washers suspended in the end of the string, the centripetal force also will increase proportionally, as the total mass will increase.

The equation for centripetal force f = mv²/r

So as mass m increase ,f also increase.

The time period of a circular motion is given by ,

T = 2πr / w

Where w is the angular velocity, and r is the radius.

So as long as angular velocity is a constant, the time period of the mass will not change.

That is Time period won't change with mass if we maintain the angular velocity.

If angular velocity is not a constant in the system, then according to the conservation of angular momentum, the angular velocity will decrease upon increasing mass.

So according to the previous equation,

T = 2πr /w , the time period T will increase.

We have the previous equation,

Centripetal force F = mV² /r

Where m is the mass , v is the velocity of rotation and r is the radius.

So as per the equation, centripetal force will increase upon increasing mass , as they are directly proportional to each other.

But the centripetal force will decrease upon increasing the radius. Because they are inversely proportional according to the equation.

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