# Glider and vertical circle question

1. Apr 27, 2016

1. The problem statement, all variables and given/known data
What is the minimum speed that a glider must fly in order to make a perfect vertical circle in the air if the circle has a radius of 200.0 m?

2. Relevant equations
Fc = mv2 / r
V = 2(Pi)r / T
3. The attempt at a solution
I have drawn the free body diagram and I think that the formula should be Fg = mv2 / r but I am confused why there is no mass given in the question. Is there a way that I can solve for the mass?

2. Apr 27, 2016

### drvrm

think about the lowermost point and the topmost point of the vertical circle the glider is going to cover - and try to find the speed it must have at both the points- the glider speed usually varies as he mounts the circle.

3. Apr 27, 2016

### rcgldr

Seems there is missing information. What is the minimum speed for the glider to be able to fly inverted in level flight (generating (- m g) of lift)?

4. Apr 27, 2016

### lychette

the question asks for the MINIMUM speed to complete the vertical circle so the ACCELERATION at the top of the circle must equal 'g' ( g= v2 /r ).
The best way to solve this problem is to consider KE and PE.
At the top the KE must equal the gain in PE (h = 2r !!!!) plus some KE to complete the circle.

5. Apr 27, 2016

### lychette

the solution is independ

the solution is independent of mass !!! acceleration is the important quantity

6. Apr 27, 2016

### rcgldr

The problem statement is a glider flying in a vertical circle. At the top, the acceleration only needs to be equal to v2 / r, where r is the radius of the circle, and with the glider generating negative lift (upwards force on inverted glider), the centripetal acceleration can be less than 1 g, with a corresponding lower speed.

Last edited: Apr 27, 2016
7. Apr 27, 2016

### CWatters

+1

8. Apr 29, 2016

### lychette

considering this is an introductory physics question I think this question is OK....not perfect maybe.
It seems straight forward to me to consider the glider flying so that the lift force is always directed towards the centre of the circle. The minimum speed would correspond to the lift at the top of the circle becoming zero which gives the centripetal acceleration at the top to be v2/r.
The KE at the bottom of the circle should equal mgh so v at the bottom is √2gh
For the values in this question I got the v at the bottom to be 90 ms-1 and the required v at the top to be 44 ms-1
So I would say the minimum speed is 134 ms-1

9. May 2, 2016