Answer:
Minimum velocity =8.57 [tex]\frac{m}{sec}[/tex]
Explanation:
To just complete vertical circular motion ball must cross the topmost point of circle with non zero tension.
So at topmost point make free body diagram showing all forces on ball.
For minimum velocity make tension zero at top point
[tex]\frac{m*v^{2} }{r}[/tex] =mg
⇒ v= [tex]\sqrt{gr}[/tex]
Now do mechanical energy conservation as work done by tension is zero all the way
Let initial velocity be v
[tex]\frac{1}{2} mv^{2} =mg(2r) + \frac{1}{2} m\sqrt{gr} ^{2}[/tex]
v = [tex]\sqrt{5gr}[/tex]
Now plug in the values
v= [tex]\sqrt{5*9.8*1.5}[/tex]
v= 8.57 [tex]\frac{m}{sec}[/tex]
In a vertical circular motion If the distance is measure from a fixed point is, it will be same at each point.
The minimum velocity that the ball must have to make it around the circle is 8.57 m/s.
In a vertical circular motion If the distance is measure from a fixed point is, it will be same at each point.
Given information-
The radius of the vertical circle is 1.5 m.
As the ball rotates in the vertical circular motion with constant velocity. Thus the speed of the ball will be same for each point.
Therefore the centripetal force should be same for each point which is,
[tex]\dfrac{mv^2}{R}[/tex]
Here, m is the mass v is the velocity and R is the radius.
This centripetal force is balanced by the tension action on the ball (towards the center) and the gravitational force acting on it. Thus,
[tex]\dfrac{mv^2}{R}=T+mg[/tex]
For the minimum velocity, the value of tension should be zero. Thus,
[tex]\dfrac{mv^2}{R}=mg[/tex]
Simplify it as,
[tex]\dfrac{v^2}{R}=g\\v=\sqrt{Rg}[/tex]
Suppose the initial velocity is [tex]v[/tex]. Thus,
[tex]\dfrac{1}{2}mv^2=mg(2R)+\dfrac{1}{2}m(\sqrt{gR}^2)\\v=\sqrt{5gR}[/tex]
The value of [tex]g[/tex] is 9.8 m/s squared. Thus, the minimum velocity that the ball must have to make it around the circle is,
[tex]v=\dqrt{5\times9.8\times1.5}\\v=8.57\rm m/s[/tex]
Hence, the minimum velocity that the ball must have to make it around the circle is 8.57 m/s.
Learn more about the vertical circular motion here;
https://brainly.com/question/10493657
