00:01
The minimum speed required at the top of the coaster to complete the loop must be such that the gravitational force equals the centripetal force and the gravitational force can be written as the mass times the gravitational acceleration whereas the centripetal force can be written as m v minimum square over r here are r is the radius of the loop in the coaster.
00:39
Now on rearranging for v minimum, the whole square, we get mgr over m.
00:50
Cancelling m on the numerator and denominator we get v minimum square to be equal to gr.
00:59
Let's call this equation 1.
01:01
Now, in our problem it is given that the speed at the top is twice of the minimum speed.
01:12
Now, using conservation of energy, we can say that the kinetic energy at the bottom plus the potential energy at the bottom must be equal to the kinetic energy at the top plus the potential energy at the top.
01:28
And this is because the total mechanical energy is conserved.
01:38
Here, the kinetic energy at the bottom can be written as half mv square, where v is the speed at the bottom.
01:47
And the potential energy is zero at the bottom...