A 2 kg block is pushed against a spring ($k=500$ N/m), compressing it by 0.2 m. If released from rest, determine the velocity of the block when it loses contact with the spring (at the unstretched position). Neglect friction.

A 10 kg block is sliding on a horizontal rough surface with an initial velocity of $v_1 = 5 \text{ m/s}$. The coefficient of kinetic friction between the block and the surface is $\mu_k = 0.3$. Determine how far the block slides before coming to rest.

An electric motor hoists a $500 \text{ kg}$ crate upwards with a constant velocity of $2 \text{ m/s}$. The motor's input power is $15 \text{ kW}$. Determine the mechanical power developed by the motor and its overall efficiency.

A pendulum is released from an angle $\theta_0$. Theoretically, if air resistance and pivot friction are completely neglected, the pendulum will swing continuously between $\theta_0$ and $-\theta_0$. However, in a real-world setting, the pendulum's amplitude gradually decreases until it stops. Analyze this phenomenon using the principle of work and energy, distinguishing between conservative and non-conservative forces.

Consider a roller coaster car approaching a vertical loop. In a previous section, we analyzed the minimum speed required at the top of the loop to prevent falling using Newton's Second Law. Now, analyze the minimum initial height $h$ the car must be released from (starting from rest) to successfully complete the loop, assuming no friction.