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Having a Ball with Newton in Floobleland (Posted on 2021-07-22) Difficulty: 3 of 5

An 80 kg ball is on a flat, horizontal, straight path in Floobleland, where the acceleration of gravity is exactly 9.807 meters/sec/sec, and there is no friction or air resistance or any other such complication. Objects also have no rotating inertia.

How far does the ball roll (meters), and how long does it take to do so (seconds) if the ball starts at rest and the following 7 events occur in sequence? (Note: each event immediately follows the previous, and the final conditions for each are the initial conditions for the next).

1) A Flooble force causes a constant acceleration of 0.1 meters/sec/sec until its speed is 20 meters/sec
2) There is a Flooble zone that lowers the speed limit. Therefore, the ball does a constant deceleration to one half of its speed over a distance of 750 meters
3) A Floobleoid starts pushing the ball. This adds a 5 Newton assist to accelerate the ball for 320 seconds
4) The ball rolls off the edge of the Flooble Canyon, which is a sheer vertical cliff of height exactly 490.35 meter. After it hits the bottom in the flat and level Flooble Valley, it's vertical speed is immediately zero and it continues on for an additional 150 seconds
5) The ball encounters a Flooble battery and immediately gains 30 Watt-hours of kinetic energy. It then rolls on for 1200 meters
6) The ball encounters a null-Flooble-energy-field and experiences no forces of any kind for 60 seconds
7) The ball Flooble-decelerates at a constant rate to a stop in 15 seconds, or, maybe in 500 meters – whichever stops the ball more quickly.

  Submitted by Kenny M    
Rating: 3.5000 (2 votes)
Solution: (Hide)
The solution can be found by analyzing each segment separately and adding the results, using various formulations of Newtons laws. For below “t” = time in seconds, “x” =distance in meters. All units in the solution are meters, seconds, kilograms

1) 20 meters/sec is reached at t=200, x=2000
2) 10 meters/sec is reached after an additional t=50, x=750
3) A speed of 30 meters/sec is reached after an additional t=320, x=6400
4) Slightly tricky – the fall off the cliff does not affect the 30 meter/sec horizontal speed of the ball, but you do need to figure out the length of time of the fall under the influence of gravity, (which is 10 seconds). Add this to 150. Additional t=160, x=4800. The ball’s speed is still 30 meters/sec
5) Another slight trick. 30 Watt-hr = 108,000 Watt-sec (or Newton-meter). Add this to the preexisting kinetic energy of the ball, which is 36,000 Newton-meter. There is now 144,000 Newton-meter of kinetic energy, which means the speed of the ball is 60 meters/sec for this entire segment. Additional t=20, x=1200.
6) No forces means no change in speed. Constant speed of 60 meters/sec for 60 seconds. Additional t=60, x=3600
7) The ball stops in 15 sec. after 450 meters, which is shorter and faster than stopping in 500meters. Additional t=15, x=450

Totals: t=825 seconds, x=19200 meters

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(7): attemptKenny M2021-07-24 07:32:22
re(6): attemptSteven Lord2021-07-23 18:50:03
re(5): attemptKenny M2021-07-23 17:46:01
re(4): attemptSteven Lord2021-07-23 14:19:44
re(3): attemptKenny M2021-07-23 12:57:31
re(2): attemptSteven Lord2021-07-23 12:37:40
re: attemptKenny M2021-07-23 05:50:58
attemptSteven Lord2021-07-22 21:50:54
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