A boy starts from point A and walks 3 meters toward the south, then turns around and walks 7 meters toward the north. What is th
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ANSWER:
(a) 1036 N
(b) -1036 N
(c) 2590 N
STEP-BY-STEP EXPLANATION:
Given:
Mc = 1400 kg
Mt = 560 kg
a = 1.85 m/s^2
(a)
Force by car on trailer:
(b)
(c)
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:
.