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

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

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

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

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

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.

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

The change in momentum depends on a square root relationship between speed and velocity().

Momentum doubles every time when velocity doubles().

It doesn't affect momentum as long as gravity remains unchanged().

Momentum increases linearly with speed since $p=mv$().

Periodic exchange between greater potential and lesser kinetic energies reflecting oscillatory motion.

Decrease in both potential and kinetic energies due to conversion of mechanical energy into thermal energy.

Constant mechanical energy as air resistance does work equal to the work by gravitational forces.

Increase in potential energy is less than the decrease in kinetic energy due to work done against air resistance.

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

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.

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.

It creates convective currents that add external work onto the pendulum system inconsistently per cycle.

Increased air viscosity from higher temperatures can enhance dissipative losses incrementally over time.

It induces thermal expansion altering pendulum length and thus its potential energy at peak swing height.

Higher temperature produces increased molecular vibrations that can amplify existing motions via resonance effects intermittently during cycles.