Gravitation in AP Physics C: Mechanics

The square root of twice gravity times height

Change in kinetic energy of the object

The product of mass and height change in the object

The product of mass and velocity of the object

Potential energy quadruples following a square-law relationship with universal constants like G.

Potential energy remains unchanged since only relative mass affects potential energy between two points.

Potential energy halves given that an increased G leads inversely proportional results for $U = -Gm_{1}m_{2}/r$.

Potential energy doubles as it is directly proportional to G within the formula $U = -Gm_{1}m_{2}/r$.

They will have identical periods due to Kepler's third law assuming circular orbits around similar-sized stars.

The heavier planet will have a shorter period due to greater gravitational attraction from the star.

The lighter planet will have a longer period due to lower inertial resistance when navigating through space.

They will have different periods because different planetary masses would lead to varying forces acting on each planet.

It doubles in strength.

There is no change in its strength.

It becomes twice as weak.

It becomes one-fourth as strong.

The slower object reaches a higher maximum height due to inertia retaining vertical momentum longer against weaker high-altitude gravity forces.

Both reach the same maximum height, since gravity acts equally irrespective initial velocities.

Maximum heights depend exclusively upon objects' weights; heavier ones pulled back down quicker, thereby ascending less far overall comparatively speaking against lighter counterparts, opposite effect observed hereby manifesting itself conversely related scenario present case under review examination scrutinization inspection contemplation observation study investigation scrutiny analysis evaluation judgement assessment appraisement appraisal reckoning determination estimation computation calculation measurement quantification enumeration tallying totaling summing adding counting reciting listing cataloguing inventorying indexing recording registering chronicle-ing documenting filing registering storage archiving conserving preserving retaining saving stashing caching hoarding stockpiling amassing collecting accumulating gathering compiling assembling organizing arranging systematizing methodizing ordering structuring configuring formatting aligning positioning sequencing sorting ranking classifying grouping batching clustering bunching corralling marshalling arraying deploying dispersing distributing spreading broadcasting disseminating promulgating publishing issuing releasing unveiling introducing showing presenting launching debuting premiering opening inaugurating commencing starting beginning initiating proceeding progressing advancing moving going coming arriving entering appearing materializing emerging sprouting arising springing emanating stemming deriving resulting ensuing following succeeding superseding replacing surmounting overcoming conquering vanquishing defeating subduing overpowering triumphing over prevailing winning mastering best achieving accomplishing executing performing completing finishing ending terminating halting stopping ceasing discontinuing concluding wrapping up shutting down calling off cutting off breaking off knocking off packing in putting away putting out turning out extinguishing snuffing dousing quenching smothering.

The object with greater launch speed reaches higher maximum height, as kinetic energy converts into gravitational potential energy during ascent.

It doubles.

It increases by a factor of four.

It decreases by a factor of four.

It decreases by a factor of two.

It increases by a factor of four.

It remains unchanged.

It doubles.

It decreases by a factor of four.

Omitting consideration for friction leads us mistakenly anticipate faster ring dispersal rates due to the absence of energy loss through heat generation.

Ignoring frictional forces could overlook energy dissipation mechanisms crucial for explaining gradual changes like tidal locking or ring system stability.

Disregarding friction assumes perfect elasticity during collisions and interactions within rings or between moons causing unrealistic perpetual motion predictions.

By neglecting frictional forces we may falsely predict more chaotic systems without appreciating how these dissipative processes contribute to long-term stability.

Such an assumption would imply that days on planets are longer than they actually are due to increased orbital circumference.

Planetary rotation periods would appear synchronized with their revolutions, which isn't usually observed in reality.

It suggests that planets experience equal solar heating throughout their orbits, which contradicts observed temperature fluctuations based on proximity to the sun.

The calculated speeds at various points in their orbits would remain constant, ignoring their true elliptical nature with variable speeds.

It increases proportionally with increased mass.

It increases exponentially with increased mass.

It decreases inversely with increased mass.

It remains unchanged regardless of increased mass.