'Suppose your hand moves upward by 0.50m while you are throwing the ball. The ball leaves your hand with an upward velocity of 2
0.0 m/s. Find the magnitude of the force (assumed constant) that your hand exerts on the ball. Ignore air resistance.' Now my question is not 'What is the magnitude' but rather: why did I get (roughly) the same answer using F=ma when you were supposed to use the total mechanical energy (W+K1+U1=K2+U2). So I'm more confused about how the 2 formulas are 'related', what the force actually represents in both, when to use what and if there is an actual difference.
1 answer:
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The change in potential energy of an object is given by
where
m is the mass of the object
g is the gravitational acceleration
is the increase in altitude of the object
In our problem,
is the mass of the book, 
and
is the increase in altitude of the book, so its variation of potential energy is
where
m is the mass of the object
g is the gravitational acceleration
In our problem,