Consider a conical pendulum with an 80.0-kg bob on a 10.0-m wire making an angle of 5.00 with the vertical as shown. Determine (a) the horizontal and vertical components of the force exerted by the wire on the pendulum and (b) the radial acceleration of the bob.

Answer 1

You will find the answers here:
http://en.wikipedia.org/wiki/Conical_pendulum

Answer 2

The forces acting on the pendulum in the vertical direction must
be in balance since the acceleration of the bob in this direction is
zero. From Newton’s second law in the y direction,
Fy Σ = T cosθ −mg = 0

Answer 3

The forces acting on the pendulum in the vertical direction must
be in balance since the acceleration of the bob in this direction is
zero. From Newton’s second law in the y direction,
Fy Σ = T cosθ −mg = 0

Solving for the tension T gives
T = mg
cosθ
=
(80.0 kg)(9.80 m s2 )
cos 5.00°
= 787 N
In vector form,
T
= T sinθ ˆi +T cosθ ˆj
= (68.6 N)ˆi +(784 N)ˆj
(b) From Newton’s second law in the x direction,
Fx = T sinθ = mac Σ
which gives
ac = T sinθ
m
= (787 N)sin5.00°
80.0 kg
= 0.857 m/s2
toward the center of the circle.
The length of the wire is unnecessary information. We could, on
the other hand, use it to find the radius of the circle, the speed of
the bob, and the period of the motion.