Hw2-2 - show all your work, including the equation, express all answers in base units, (m, m/s, m/s2), unless stated otherwise i
1 answer:
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Answer:
The force exerted by the ball on the bat has a magnitude of 100 N and its direction is exactly opposite to that of the force exerted by the bat on the ball.
Explanation:
Recall that Newton's third law tells us that : "For every action, there is an equal and opposite reaction."
Therefore if the bat acts on the ball with a force of 100 N, the ball acts on the bat with a similar magnitude of force (100 N) but direction opposite to the original force.
Answer:
, assuming that
and
are point charges.
Explanation:
Let denote the coulomb constant. Let
denote the distance between the two point charges. In this question, neither
and
depend on the value of
.
By Coulomb's Law, the magnitude of electrostatic force between and
would be:
.
Find the first and second derivative of with respect to
. (Note that
.)
First derivative:
.
Second derivative:
.
The value of the coulomb constant is greater than
. Thus, the value of the second derivative of
with respect to
would be negative for all real
.
would be convex over all
.
By the convexity of with respect to
, there would be a unique
that globally maximizes
. The first derivative of
with respect to
should be
for that particular
. In other words:
<em>.</em>
.
.
In other words, the force between the two point charges would be maximized when the charge is evenly split:
.