A pendulum consisting of a small heavy ball of mass m at the end of a string of length l is released from a horizontal position. When the ball is at point P, the string forms an angle 30 degrees with the horizontal.
a. Free body diagram (all set on that)
b. Determine the speed of the ball at P.
c. Determine the tension in the string when the ball is at P.
d. Determine the tangential acceleration of the ball at P.
PEi + KEi = PEf + KEf
a = v^2 / r
Fc = mv^2 / r
The Attempt at a Solution
a. was just drawing a free body diagram, easy. For b., PE = KE, mglsin(30) = .5mv^2, v^2 = gl, v = sqrt(gl).
For c., is it just that the tension is equal to the centripetal force? In that case, Ft = Fc = mv^2/r = mv^2/l = mg? It just seems strange that it's the same as the force due to gravity at this point.