Physics Ninja: Mastering Work, Energy, and Power

Apply the extended work energy theorem to a gravity–spring system, showing that the work by gravity and the spring equals changes in kinetic energy and total mechanical energy remains conserved.

apply conservation of energy to a 3 kg mass released from 5 m on a curved frictionless ramp with a 400 N/m spring, yielding x ≈ 0.86 m.

Analyze a 2.4 kg block dropped from five meters onto a spring, derive the spring constant from maximum compression, and find speed at 15 cm using energy conservation (no friction).

The lecture shows how gravity does negative work when moving a mass from the earth’s surface to three radii, with W = -2/3 GMm/R_E.

Explore power as the time rate of energy transfer, defined as work divided by the time interval, and examine how this expands the work-time relationship for constant forces.

Compute the minimum motor power to lift a fully loaded elevator at constant speed using a free-body diagram, accounting for weight and friction, then convert power to horsepower.

Practice nine multiple choice problems, mixing conceptual questions with small calculations, using the attached PTF to work before watching the solutions. Reach out with any questions via email or message.

Apply energy conservation to the pendulum: initial gravitational potential energy becomes final kinetic energy at the bottom. Compute height using 5 m rope and 53°, then v ≈ 6.3 m/s.

Compare two cases of pushing a crane on a horizontal floor: adding a child increases the normal force and kinetic friction, making w2 larger than w1 for the same displacement.

Practice nine multiple-choice energy problems, balancing conceptual questions with small calculations; download the problem set, work on the problems, then view the solutions.

Calculate the potential energy loss and power of a 50-meter waterfall with mass flow 5.5×10^6 kg s^-1, then convert to dollars per year using kilowatt-hour pricing.

Apply conservation of energy to a 2 kg book dropped from 10 m; calculate initial potential energy, final kinetic energy, and final speed of about 12.9 m/s.

Use conservation of energy on a frictionless roller coaster to compute speeds at A, B, C, D; v_B = 0, v_C = sqrt(g h), v_D = sqrt(2 g h).

Apply conservation of energy to a 2 kg block dropped from 0.40 m onto a spring to find the maximum compression; solving the energy balance yields a 0.10 m compression.

Examine how dissipated energy from air resistance lowers height for a 9.4 kg mass; equate energy loss to m g delta y to show frictionless rise is 738 meters higher.

Apply the work-energy theorem to a rock sliding down a slope with friction, computing gravitational potential energy, frictional work, and the final speed using the normal force.

Apply the work-energy theorem to a two-block system connected by a string, accounting for constant gravity, friction, tension, and normal forces to find the final speed after distance L.

Use energy conservation in a frictionless pulley with two masses and a spring on an incline to determine speeds of both blocks when the spring returns to unstretched length.