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Gravitational potential energy is the energy an object possesses because of its position in a gravitational field. It is dependent on three main factors: the object's mass (\( m \)), the height (\( h \)) of the object above a reference level, and the acceleration due to gravity (\( g \)), which is approximately \( 9.81 \,\mathrm{m/s^2} \) on Earth. This potential energy is mathematical expressed as \( U = mgh \).

For instance, in the problem we are exploring, when the pebble is held \( 70 \) meters above the waterline, its gravitational potential energy can be calculated. When calculating or comparing gravitational potential energy, it's crucial to set a baseline, or point of zero potential energy. In our example, the waterline is initially set as this zero point.

Understanding these concepts is essential, not only for calculating the gravitational potential energy at various positions but also for comprehending how energy transformations occur during a free fall.

Work done by gravity involves the energy transferred to or from an object by the gravitational force as it moves a certain distance. It is closely related to gravitational potential energy because any change in gravitational potential energy corresponds to work being done by gravity. The formula to calculate this work is similar to that for gravitational potential energy: \( W = mgh \). This signifies that the work done by gravity is essentially the energy shift as an object moves from one point to another vertically.

In our exercise, the pebble falls from a height of \( 70 \) meters to a net located \( 3 \) meters above the water. By calculating \( mgh \) for this height difference, we find that the work done by gravity is \( 34.285 \, \mathrm{J} \). This represents the energy gravity has transferred to the pebble during its descent, emphasizing the powerful role gravity plays in influencing motion and energy distribution.

Solving physics problems, like the one involving the falling pebble, requires understanding the underlying principles of physics concepts such as gravitational potential energy and work.

A typical problem-solving approach includes identifying:

• All given data, like the pebble's mass and height.
• The formulas applicable to the problem, such as \( W = mgh \).
• The conditions, like what is defined as zero potential energy.

Developing a systematic approach to physics problems helps in breaking down complex concepts into manageable calculations, ensuring a step-by-step resolution. Most importantly, interpreting the physical meaning of the results is key, as seen when calculating how energy changes and is impacted by various positions and influences. Practicing these components strengthens proficiency not just in dealing with numbers but in grasping how fundamental forces like gravity practically operate in our world.