The figure below shows three uniform objects: a rod with m1 = 7.00 kg, a right triangle with m2 = 3.70 kg, and a square with m3
= 5.30 kg. their coordinates in meters are given. determine the center of gravity for the three-object system.
1 answer:
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Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for such that
is maximized. Once we have that
, we can easily find the answer to part b.
Finding the value that maximizes is the same as finding the value that maximizes
, just on a smaller scale. So, we really want to maximize
. To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of such that the inner part of the square term is equal to
.
.
So, the answer to part a is .
We can then plug into the equation for p to find the answer to part b.
.
So, the answer to part b is .
And we're done!