Determine the minimum coefficient of static friction that must be there between Howard's shoe and the court, so that he does not slip? (Shoe manufacturers pay close attention to such requirements.) Round the final answer to three decimal places. If Howard weighed 190 lb, rather than 275 lb, would the magnitude of the static friction force required to accelerate him at 21.6 ft/s2 be reduced? Would the resultant minimum coefficient of static friction obtained in part (a) of this problem change?
Assume that Dwight Howard weighs 275 lb and can move horizontally with an acceleration of 21.6 ft/s2. However, he would be unable to do this in slippery socks.
Determine the minimum coefficient of static friction that must be there between Howard's shoe and the court, so that he does not slip? (Shoe manufacturers pay close attention to such requirements.) Round the final answer to three decimal places.
If Howard weighed 190 lb, rather than 275 lb, would the magnitude of the static friction force required to accelerate him at 21.6 ft/s2 be reduced? Would the resultant minimum coefficient of static friction obtained in part (a) of this problem change?
a)
The minimum static force required to make Howard not slip should be equal to the force making him accelerate. Thus,
Here, Fs and F represent the static friction’s force, and the force acting on Howard, respectively.
The static friction’s force can be represented as,
Here, μs and m represent the static friction coefficient, and Howard’s mass, respectively.
Also, from Newton’s law,
Here, a represents Howard’s acceleration.
Thus,
Substitute the relevant values.
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