A huge pendulum consists of a 200Kg ball at the end of a cable 15 m long. If the pendulum is drawn back to an angle of 370 and released, what maximum force must the cable withstand as the pendulum swings back and forth?
Answers
Answer:
When the pendulum is at its lowest point, there are two forces acting on it: gravity and a centrifugal force. Both forces are directed straight down. This results in the maximum force:
Fmax=mg+mv2/rFmax=mg+mv2/r
where mm is the mass of the ball ( 200kg200kg ), vv is the velocity of the ball, g is the acceleration of gravity ( 9.8m/sec29.8m/sec2 ), and rr is the length of the pendulum (15m)(15m) . You now have all that you need to solve the problem.
Use the the angle 37∘37∘ to determine the height hh of the ball with respect to its lowest point ( 3.02m)3.02m) .
Then use the conservation of energy to determine the velocity of the ball: 12mv2=mgh⟹v=2gh−−−√.12mv2=mgh⟹v=2gh.
Finally, use the above equation for FmaxFmax to determine the maximum force.