A few Circular Motion questions?

Question

1) Two tennis balls at the ends of two strings are moving at the same speed in a horizonal circular path. Compare the magnitudes of the two centripetal acceleration.

2) A object that is 10 kg is whirled in a vertical circle with a radius of 3m at a constant speed of 8 m/s. Find the minimum and max tensions in the string.

I haven't the slightest clue as to how to approach #1 ... it seems like a trick question, lol. As for #2, what in the world is minimum tension?

Answer 1

Here is the following:

1) Centripetal acceleration : v^2/r

2) You have to balance the forces, min tension is when ball is at the top of the circle, max when it is on the bottom. You have 3 forces: tension, gravity and centripetal forces.

Answer 2

1) If the velocities are the same and the radius is the same, then the acceleration is the same.  The radius is inversely proportional to the acceleration so the bigger the radius the smaller the acceleration.  The velocity is the directly proportional to the acceleration, a high velocity will give you a higher acceleration.  a=v(squared)/r

2)Centripetal force always goes out no matter what. Since it says that its in a vertical circle the minimum tension would be at the very top where centripetal force is going out and gravity is pulling it down and the maximum tension would be at the bottom since gravity and centripetal force is going the same way.

F=ma

10 kg * 9.8 m/s*s = 98 N, this is force due to gravity

F(centripetal)= m*v*v/r

F= (10 kg * 8 m/s * 8 m/s)/3= 213.3 N

minimum = 213.3 N - 98 N = 115.3 N

maximum = 213.3 N + 98 N = 311.3 N

Hope this Helps!