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24. The following reasoning leads to an apparent paradox; explain what’s
wrong with the logic. A baseball player hits a ball. The ball and the bat
spend a fraction of a second in contact. During that time they’re moving
together, so their accelerations must be equal. Newton’s third law says that
their forces on each other are also equal. But a=F/m, so how can this be,
since their masses are unequal. (Note that the paradox isn’t resolved by
considering the force of the batter’s hands on the bat. Not only is this
force very small compared to the ball-bat force, but the batter could have
just thrown the bat at the ball.)
25. Driving down a hill inclined at an angle
.
with respect to horizontal,
you slam on the brakes to keep from hitting a deer. (a) Analyze the forces.
(Ignore rolling resistance and air friction.) (b) Find the car’s maximum
possible deceleration, a (expressed as a positive number), in terms of g,
.
,
and the relevant coefficient of friction. (c) Explain physically why the car’s
mass has no effect on your answer. (d) Discuss the mathematical behavior
and physical interpretation of your result for negative values of
.
. (e) Do
the same for very large positive values of
.
.