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t that instant, find the magnitude of the acceleration of the bowling ball and the tension in the rope.?
A bowling ball weighing 71.2 N is attached to the ceiling by a 3.80 m rope. The ball is pulled to one side and released; it then swings back and forth like a pendulum. As the rope swings through its lowest point, the speed of the bowling ball is measured at 4.00 m/s
Use Newton’s 2nd law to write an equation for the net centripetal forces on the ball is it swings through its arced path:
∑F = mv²/r = T - mg
T = m[(v²/r) + g]
The mass of the ball is:
m = w/g
= 71.2N / 9.80m/s²
= 7.27kg
So:
T = 7.27kg[(16.0m²/s² / 3.80m) + 9.80m/s²]
= 102N
Hope this helps.
Later noticed you needed the acceleration as well. It is centripetal and is:
a = v²/r
= 16m²/s² / 3.80m
= 4.21m/s²
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