ok a person is holding onto a piece of string
at the end of the string is a ball
the person whrils it around in a circle
i've been asked what's the mininum value of at the top of the circle (this is swung around in a verticle circle) what is the mininum value the velocity could be to keep it moving in a circle
ok i found it my only question is why is the speed at the bottom given as twice the mininum speed at the top
then from there it says solv efor the force of tension at the bottom which i know how to do once i know why i can multiply the minninum speed at the top by two
Vertical circle? At the top, tension has to equal the force of centripetal acceleration (minus weight) or
Tension=mv^2/r -mg
IF tension is zero,
v= sqrt (rg) that is the minimum value.
so if v = sqrt(rg), then the KE at the top is 1/2 m rg. the PE at the top is 2mgr
So it falls to the bottom, total energy is 1/2 mrg+2mgr. All that energy is in KE, as PE is zero.
1/2mv^2=1/2mrg+2mgr=2.5 mrg
v=sqrt(5gr) which is slightly more than twice the speed at the top.
hyperphysics.phy-astr.gsu.edu/HBASE/mechanics/cirvert.html
check my thinking and math.
hey wow thanks!!!
I acutally understood
just kind of werid because our book hasn't mentioned energy yet but I know about it from just regualr old physics
I'm taking ap this year and doing the first chapters in order and it hasn't mentioned anything about energy yet just told me it was twice but not why
Thanks =]
To understand why the speed at the bottom of the circle is given as twice the minimum speed at the top, we need to consider the forces acting on the ball during circular motion.
1. Centripetal Force: In order for an object to move in a circle, there must be a force acting towards the center of the circle called the centripetal force. In this case, the tension in the string provides this force, keeping the ball moving in a circular path.
2. Gravity: Another force acting on the ball is gravity, which always acts vertically downward towards the Earth.
At the topmost point of the circle, the tension in the string should be just sufficient to provide the required centripetal force to keep the ball moving in a circle. This minimum tension occurs when the ball is momentarily at rest at the top, meaning its velocity is zero. At this point, the only force acting on the ball is gravity. The tension in the string must counterbalance the force of gravity to keep the ball from falling.
As the ball moves towards the bottom of the circle, the tension in the string needs to increase to counterbalance both gravity and provide the required centripetal force. This is because, at the bottom, the centripetal force and gravity act in the same direction and need to be added together.
The minimum speed at the top occurs when the tension in the string is just enough to counterbalance gravity. At the bottom, the tension in the string needs to provide both the centripetal force and counterbalance gravity. Since the tension at the bottom of the circle needs to be greater than the minimum tension at the top, the minimum speed at the top needs to be multiplied by at least 2 to meet the requirements of both forces.
To solve for the tension at the bottom of the circle, once you have calculated the minimum speed at the top, you can use the equation:
Tension at the bottom = (mass * velocity^2) / radius + mass * gravity,
where mass is the mass of the ball, velocity is the minimum speed at the top (multiplied by 2), radius is the radius of the circular path, and gravity is the acceleration due to gravity.