Energy

It exceeds its original height as air resistance adds kinetic energy during upward motion.

It reaches less than its original height because air resistance removes some mechanical energy from the system.

Its height remains unaffected as air resistance evenly slows down both upswing and downswing phases.

It returns to its original height because gravitational potential converts fully back-and-forth between kinetic and potential energies.

The actual temperature deltas depend specifically on the details of those particular cycles, but an approximation through the equivalent efficiency of the Carnot principle enables us to use the expression $T_{\text{high}} - T_{\text{low}} = T_{\text{high}} \times (e - 1)$.

Inocentia Ficantia.

Inocentia Fictions.

Inocentia Ficantes.

The overall resistance decreases.

The overall resistance increases.

The overall resistance remains unchanged.

The overall resistance becomes half of the original resistance.

Cos⁻¹(½)

Cos⁻¹(¼)

Cos⁻¹(⅓)

Cos⁻¹(⅔)

Initial elastic potential in spring minus work done against friction equals zero net work when stopped.

Kinetic friction alone sets distance limited by static coefficient times normal force for starting motion only.

Gravity solely dictates travel length since it acts constantly upon mass regardless of surface interactions.

Only mass-dependent inertia determines distance since all objects move equally against kinetic friction if launched similarly.

Elastic potential energy stored within the pendulum string or rod itself.

Thermal energy resulting from air resistance during swing.

Kinetic energy, due to the pendulum's motion reaching maximum speed at the peak.

Potential energy, since height above reference level is greatest at this point.

The kinetic energy doubles.

The potential energy becomes zero.

The total mechanical energy remains constant.

The mechanical energy increases over time.

3900 J

19130J

2295540J

38259 J

No net work is done by gravity since total mechanical energy remains unchanged throughout descent.

Negative work is done by gravity because overall mechanical energy seems reduced due to decrease in height.

Positive work is done by gravity since displacement occurs in direction of gravitational force vector.

Gravity does increasing work until midpoint of descent then decreasing work afterwards during continuation towards lower track segment.

$\frac{v_0^2}{g}$

$\frac{v_0^2}{4g}$

$\frac{3v_0^2}{4g}$

$\frac{v_0^2}{6g}$