An object attached to the end of a string?

Question

An object attached to the end of a string
swings in a vertical circle of radius 2.6 m as
shown. At an instant when theta=31 degrees, the speed
of the object is 13 m/s and the tension in the
string is 60 N.
The acceleration of gravity is 9.8 m/s^2 :

What is the mass m of the object? Answer
in units of kg.

Answer 1

There are two forces on that mass m, force of gravity W and centripetal force Fc. These forces are related to tention T as

Fc=Tsin(31)
W=Tcos(31)
and


Fc= ma where a = V^2/R

then m= Fc/(V^2/R)
m= R T sin(31) / V^2
m= 2.6 x 60 sin(31) / (13)^2=
m=0.48 kg