Question

consider the motion of a sledder shown in the diagram below. the kinetic energy (ke) and potential energy (pe) values are shown for various locations. in this example, ______. include all that apply.
a. kinetic energy is conserved
b. potential energy is conserved
c. total mechanical energy is conserved
d. none of the above are true.
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Explanation:

Step1: Calculate total mechanical energy at each location

Total mechanical energy \(E = KE+PE\).

• At \(A\): \(E_A=3000 + 12000=15000\space J\)
• At \(B\): \(E_B=9000 + 6000=15000\space J\)
• At \(C\): \(E_C=15000+0 = 15000\space J\)
• At \(D\): \(E_D=12000 + 3000=15000\space J\)
• At \(E\): \(E_E=15000+0=15000\space J\)

Step2: Analyze conservation of energies

• Kinetic energy (\(KE\)) values: \(3000\space J\) (at \(A\)), \(9000\space J\) (at \(B\)), \(15000\space J\) (at \(C\)), \(12000\space J\) (at \(D\)), \(15000\space J\) (at \(E\)) are not the same. So, kinetic energy is not conserved.
• Potential energy (\(PE\)) values: \(12000\space J\) (at \(A\)), \(6000\space J\) (at \(B\)), \(0\space J\) (at \(C\)), \(3000\space J\) (at \(D\)), \(0\space J\) (at \(E\)) are not the same. So, potential energy is not conserved.
• Total mechanical energy \(E = 15000\space J\) at all locations (\(A\), \(B\), \(C\), \(D\), \(E\)). So, total mechanical energy is conserved.

Answer:

C. total mechanical energy is conserved