Consider a conical pendulum with an 82.4kg bob on a 12.8m wire making an angle θ of 6.70° with the vertical. Determine the horizontal and vertical components of the force exerted by the wire on the pendulum. Enter the horizontal component first and then the vertical component. Calculate the radial acceleration of the bob.
+33616 Let tension in the wire be T, mass be m, velocity be v, length of wire be L, radius be r and gravitational acceleration be g.
Resolve forces horizontally and vertically.
Vertical: Tcos(θ) = mg ...(1)
Horizontal: Tsin(θ) = mv2/r ...(2)
The radial acceleration is v2/r = Tsin(θ)/m = g*sin(θ)/cos(θ) = g*tan(θ) using (1) and (2)
Plug in the numbers!
+33616 Let tension in the wire be T, mass be m, velocity be v, length of wire be L, radius be r and gravitational acceleration be g.
Resolve forces horizontally and vertically.
Vertical: Tcos(θ) = mg ...(1)
Horizontal: Tsin(θ) = mv2/r ...(2)
The radial acceleration is v2/r = Tsin(θ)/m = g*sin(θ)/cos(θ) = g*tan(θ) using (1) and (2)
Plug in the numbers!
