Question

'Suppose your hand moves upward by 0.50m while you are throwing the ball. The ball leaves your hand with an upward velocity of 20.0 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.

Answer 1

The formula $F = ma$ is used when the statement of second law of motion is applied to the problem. If the statement is applied to the problem, The fomula will be used. If not, use the formula $W + K_{1} + U_{2} = K_{2} + U_{2}$