Question

You swing one yo-yo around your head in a horizontal circle. then you swing another yo-yo with twice the mass of the first one, but you don't change the length of the string or the period. how do the tensions in the strings differ?

Answer 1

`F'=2* F`

Step-by-step explanation:

You swing one yo-yo around your head in a horizontal circle. The tension acting in the string is equal to the centripetal force. Its formula is given by :

`F=(mv^2)/(r)`

r is the radius of circular path or the length of the string. It remains constant. If the mass of the yo- yo swing is double such that, m' = 2m

New centripetal force is equal to,

`F'=(m'v^2)/(r)`

`F'=(2mv^2)/(r)`

`F'=2* (mv^2)/(r)`

`F'=2* F`

So, the new tension in the strings gets doubled.

Answer 2

The tension on the second yoyo is twice as large as the tension with the first yoyo. The tension you notice on the string of the yoyo is due to centripetal force. The equation for how much force you have is F = m*v^2/r Since in the problem, the only change you made to the system was a doubling of the mass, it will cause the overall force to double.