Circular motion: finding the centripetal acceleration without mass, velocity, or tension given

Question

I can't seem to solve this question... A ball is swung in a horizontal circle so that the string makes a 26º with the pole it is attached to. What is the centripetal acceleration?

Answer 1

The 26° angle is from the vertical.  Call it θ.  The horizontal component of the tension is the centripetal force in this problem.  The vertical component of the tension must equal the weight.

 

F_c = T sinθ

 

mg = T cosθ ⇒ 

 

T = mg/cosθ

 

a = F_c/m = T sinθ / m = (mg/cosθ)sinθ / m = g tanθ

 

Note that in this problem, a does not depend on the mass, velocity, or tension; just on the angle.