How Do Key Swings Maintain a Circular Path?

[farhannaeem]

Keys with a combined mass of 0.100 kg are attached to a 0.25m long string and swung in a circle in the vertical plane.
a) What is the slowest speed that the keys can swing and still maintain a circular path?
b) What is the tension in the string at the bottom of the circle?

 

[praharmitra]

Show what you have done and where you are stuck.

 

[farhannaeem]

i don't know how to approach it like how to start the problem

 

[tiny-tim]

start by writing out all the equations you know that might help

(if you don't know any, go back to your book or your lecture notes and find some)

 

[rwisz]

a) The slowest speed that the keys can swing and still maintain a circular path can be calculated using the equation v = √(gr), where v is the minimum velocity, g is the acceleration due to gravity (9.8 m/s^2), and r is the radius of the circular path (0.25m). Therefore, the minimum velocity would be approximately 0.7 m/s.

b) At the bottom of the circle, the tension in the string can be calculated using the equation T = mg + mv^2/r, where T is the tension, m is the mass of the keys (0.1 kg), g is the acceleration due to gravity, v is the velocity, and r is the radius of the circular path (0.25m). Assuming the minimum velocity of 0.7 m/s, the tension at the bottom of the circle would be approximately 1.1 N.