Asolid 0.6350 kg ball rolls without slipping down a track toward a vertical loop of radius r=0.8950 m.

what minimum translational speed vmin must the ball have when it is a height h=1.329 m above the bottom of the loop in order to complete the loop without falling off the track?

assume that the radius of the ball itself is much smaller than the loop radius r. use g=9.810 m/s2 for the acceleration due to gravity.

The minimum translation speed is 4.21 m/s.

Explanation:

Given that,

Mass of solid = 0.6350 kg

Radius = 0.8950 m

Height = 1.329 m

We need to calculate the speed of the ball

Using formula of centripetal force

Put the value into the formula

We need to calculate the minimum translation speed

Using conservation of energy

Put the value into the formula

Hence, The minimum translation speed is 4.21 m/s.

think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.