Thursday, November 24, 2016

Physics of bowling

Physics of bowling

This week I went to a bowling alley in Philadelphia and thought about physics and rotational motion while playing. I noticed that the a bowling lane is about 18 meters long and a 15-pound (6.8 kg) ball rolled for about 6 seconds before hitting the pins. The radius of a standardized 15-pound bowling ball is 8.5’’ (0.22 m)

=> v(ball) = 18/6 = 3 m/s
=> w(ball) = v/r = 3/0.22 = 13.6 rad/s = (13.6 *60)/(2π) = 130 rpm

Image result for bowling ball spinning

Image result for bowling lane

For the sake of simplicity, I assumed that the ball accelerated very briefly before entering the 18-meter lane, and throughout the 18-meter lane, it travelled at constant rotational speed.

=> a(tan) = rα = 0
     a(radial) = a(linear) = w2r = 13.62 * 0.22 = 40.7 m/s2

=> F = m*a(linear) = 6.8 * 40.7 = 276.7 N

Assuming the ball hit the top pin directly, this pin was impacted by a force of 276.7 N in magnitude, enough to knock it down along with a few pins behind.

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