Work, Energy, and Power in Physics

Decrease-in-kinetic-and-gravitational-potential-energy-as-lost-to-air-resistance

Increase-in-gravitational-potential-energy-as-falling-object-slows-down

No change occurs in total mechanical-energy as gravitational-potential converts entirely into thermal-energy-due-to-air-resistance

Kinetic-energy-is-transferred-to-the-surrounding-air-particles-increasing-their-mechanical-energy

Gravitational potential energy at a particular point

Total mechanical energy at the start of the oscillation cycle

Kinetic energy at a turning point

Potential energy stored in the oscillating spring

Quantum tunneling increases the effective collision cross-section.

Heisenberg’s uncertainty principle predicts variable post-collision velocities.

Photon emission during collisions slightly reduces system kinetic energy.

Microscopic variations in surface structure may alter collision characteristics.

$\frac{v_m}{V_M} = \frac{M}{m}$

$\frac{v_m}{V_M} = 1$

$\frac{v_m}{V_M} = \frac{M+m}{M-m}$

$\frac{v_m}{V_M} = \frac{m}{M}$

At no point; only total mechanical energy remains constant.

Halfway up the hill.

When its speed is reduced by half from that at the bottom.

At the top of the hill where it comes to rest for an instant.

Electromagnetic eddy currents opposing rotation manifest additional torque resisting motion.

Spin-orbit coupling aligns magnetic dipoles decreasing net magnetization resultant loss rates.

Magnetic fields penetrate reducing rotational inertia modifying angular velocity proportionately.

Lorentz forces induce charge separation shifting center mass adjusting precession dynamics accordingly.

Much less than predicted because all initial potential energy is lost to air resistance.

Slightly less than predicted by conservation of energy without air resistance.

Greater than predicted due to additional force provided by air resistance.

Exactly the same as predicted by conservation of energy without air resistance.

Neglecting Earth's rotation effect on pendulum motion for moderate latitudes

Considering string mass in tension calculations when it's negligible

Assuming simple harmonic motion for large $\theta_0$

Ignoring variation in $g$ with altitude for pendulums on tall buildings

Yes, but only if the springs are compressed instead of extended.

No, kinetic energy is only dependent on the mass and displacement, not the stiffness of the spring.

Yes, the displacement is both the same and the masses are identical, so their kinetic energies should be equal.

No, the mass attached to the stiffer spring will have less kinetic energy because the force required to compress it is greater.

Velocity of each object

Momentum of the system

Kinetic energy of each object

Potential energy of the system