Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 6 - Work and Energy - Check Your Understanding - Page 159: 10

Answer

All are correct.

Work Step by Step

As the total mechanical energy is conserved, we have $$E_f=E_0$$ $$KE_f+PE_f=KE_0+PE_0$$ $$KE_f-KE_0=-(PE_f-PE_0)$$ So if kinetic energy decreases, or $KE_f-KE_0\lt0$, then $PE_f-PE_0\gt0$, meaning gravitational potential energy increases, so a) is correct. If gravitational potential energy decreases, or $PE_f-PE_0\lt0$, then $KE_f-KE_0\gt0$, meaning kinetic energy increases, so b) is correct. If kinetic energy does not change, or $KE_f-KE_0=0$, then $PE_f-PE_0=0$, meaning gravitational potential energy does not change, too, so c) is correct.
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