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A billiard ball of mass 0.3 kg is struck by a cue stick which imparts a speed of 1 m/s to the ball.?
If the average force exerted by the cue stick on the ball is 10 N, the distance over which the force acted is
The force acted over 0.015 m = 1.5 cm. Here's how to show this:
The kinetic energy imparted is 1/2 m v^2 which must be the accelerative work done, that is (F_mean)*d. ###
Therefore, symbolically, d = 1/2 m v^2 / F_mean,
or in this case 1/2 (0.3) 1^2 /10 m = 0.015 m = 1.5 cm.
Live long and prosper.
### Of course, the DIRTY LITTLE SECRET about this kind of problem is that LOGICALLY, there's NO WAY to determine F_mean (or F_av) otherwise than by knowing either over WHAT DISTANCE or for WHAT TIME the force is supposed to have acted.
Just think about it: If you're an avid reader of Yahoo Answers! you have doubtless seen countless questions in which either F_mean (w.r.t total distance moved) or F_av (w.r.t total time the force is acting) are found by effectively integrating some unknown force over distance or time and then dividing by the overall length from start to finish of the relevant variable. [HOW ELSE COULD YOU DO IT ?!]
In such problems, because the distribution of force relative to distance or time could be quite different, there is thus absolutely NO reason that the quantity F_mean (w.r.t to distance) should equal F_av (w.r.t. to time).
The INESCAPABLE CONCLUSION is this: F_mean and F_av are themselves UTTERLY MEANINGLESS and otherwise USELESS except as CONSTRUCTED QUANTITIES known only once you DO KNOW the distance or time through which they act.
Thus, whoever set this question is engaging in CIRCULAR LOGIC and evidently cannot appreciate the difference between cause and effect. It's a THOROUGHLY BAD PROBLEM, the product of a SERIOUSLY DEFICIENT SCIENTIFIC EDUCATION !
Silver Cue Billiards 8 Ball Tournament: Drew Mccann & Don Robertson 02 28 2010