Question

what is the kinetic energy of a pile driver ram starting from rest that undergoes a 10-kj decrease in potential energy? options: 0 kj, -10 kj, 5 kj, 10 kj

Explanation:

Step1: Recall Energy Conservation

The law of conservation of energy states that the total mechanical energy (kinetic + potential) of a system remains constant if no non - conservative forces act. For a pile - driver ram starting from rest, initial kinetic energy \(K_i = 0\) (since \(v_i = 0\)) and let the initial potential energy be \(U_i\) and final potential energy be \(U_f\), final kinetic energy be \(K_f\). The change in potential energy \(\Delta U=U_f - U_i=- 10\space kJ\) (negative because potential energy decreases).
From the conservation of mechanical energy \(K_i+U_i = K_f+U_f\).

Step2: Solve for Final Kinetic Energy

Substitute \(K_i = 0\) into the energy conservation equation: \(0 + U_i=K_f+U_f\).
Rearrange the equation to solve for \(K_f\): \(K_f=U_i - U_f=-(U_f - U_i)\).
Since \(\Delta U = U_f - U_i=- 10\space kJ\), then \(K_f=-(- 10\space kJ)=10\space kJ\).

Answer:

10 kJ (corresponding to the option "10 kJ")