Question

A stone, of mass m, is attached to a strong sting and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the stone's weight. The stone's speed at this point is given by:________
A) (2gr)1/2
B) (gr)1/2
C) 2gr
D) 2(gr)1/2

Answer 1

Answer:

A. (2gr)1/2.

Explanation:

Solution:

Newton's second law for the stone At the exact bottom of the path:

⃗ + ⃗⃗ = ⃗ = ⃗

- stone's weight;

= 3- tension in the string;

- Centripetal force (the stone is going in a circle);

 - centripetal acceleration.

Projection on the Y-axis:

: − = (1)

at the bottom the tension is is 3 times the stone's  weight:

= 3 (2)

Formula for centripetal acceleration:

= ²/

(3)

(3)(2)(1):

3 − = ²/

2 =

²/

2 = ²

= √2

Answer: The stone's speed at the exact bottom of the path is given by = √2