Question

What would you expect to happen to the velocity of the bobber if the mass of the washers in the cylinder remained the same and the radius was doubled?

Answer 1

When the radius is doubled and the mass remains constant, the velocity of the bobber in a pendulum system would decrease, as the period of oscillation is inversely proportional to velocity. Similarly, in circular motion, the velocity would decrease to maintain the same centripetal force, since it is directly related to the square of the velocity and inversely to the radius.

Step-by-step explanation:

If the radius of the path travelled by a bobber attached to a string is doubled while keeping the mass of the washers constant, assuming that we are dealing with a simple pendulum or a centripetal motion scenario, the velocity of the bobber would be expected to change. Under pendulum conditions, the period of oscillation depends on the length of the pendulum and gravity, but not on the mass. Doubling the length (which is effectively the same as radius in this context) would increase the period, resulting in a decrease in velocity since velocity is inversely proportional to the period. In the case of uniform circular motion, if the force remains the same (here assumed by the constant mass of the washers), but the radius is doubled, the velocity would be expected to decrease to maintain the same centripetal force because the centripetal force is directly proportional to the square of the velocity and inversely proportional to the radius (Fc = mv2 / r).

Answer 2

The velocity becomes
`v\sqrt 2`.

Step-by-step explanation:

The force acting on the bobber is centripetal force.

The centripetal force is given by

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

when mass remains same, radius is doubled and the force is same, so the velocity is v'.

`F =(mv^2)/(r)=(mv'^2)/(2r)\\\\v'=v\sqrt 2`