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Understanding the potential energy formula is crucial when calculating the gravitational potential energy of an object in a physics problem. Gravitational potential energy (PE) is the energy an object possesses due to its position in a gravitational field. The standard formula for gravitational potential energy is given by:
\[ PE = mgh \]
where:

• \( m \) is the mass of the object in kilograms,
• \( g \) is the acceleration due to gravity (9.8 m/s²\ton Earth),
• \( h \) is the height above the reference point in meters.

To solve the example problem, we plug in the values for the mass of the person, the acceleration due to gravity, and the height they have jumped to calculate the increase in gravitational potential energy. It's essential to ensure that the unit of the height is converted to meters, as consistent units are fundamental for accurate calculations. The mass of the person is given as 72 kg, and the height of the jump is 60 cm, which we convert to 0.6 m. By substituting these values into the formula, we can find that the energy required for a 72 kg person to reach a height of 0.6 m is:
\[ PE = 72 kg \times 9.8 m/s² \times 0.6 m \]

The work-energy principle is a fundamental concept in physics that relates the work done on an object to the change in its energy. When work is performed on an object, it results in a transfer and transformation of energy. Work done against gravitational forces results in an increase in gravitational potential energy of an object.
In our scenario, when a person jumps, their muscles do work to propel them upward. This work is equivalent to the increase in gravitational potential energy as they reach the maximum height of their jump. The formula for work (W\ton) in terms of energy is expressed as:
\[ W = \text{Change in energy} = PE_{final} - PE_{initial} \]
If we consider the ground level as the point where the potential energy is zero (\( PE_{initial} = 0 \)), then the work done by the muscles is equal to the final potential energy at the peak of the jump (\( PE_{final} \)). This demonstrates the conversion of kinetic energy generated by the muscles into potential energy at the jump's apex.

Unit conversion is a critical step in solving many physics problems, ensuring quantities are measured in compatible units. It involves transforming a measure expressed in one set of units into another, maintaining the same quantity. In the context of our example, we need to convert the jump's height from centimeters to meters before we can use it in the potential energy formula.
This is because the standard unit for length in the International System of Units (SI) is meters (m), while the formula for gravitational potential energy requires that all units are consistent. Here's how we perform the conversion:
\[ 60 \text{cm} \tdiv 100 = 0.6 m \]
There are 100 centimeters in 1 meter, so dividing by 100 accomplishes the conversion. It's always helpful to remember some common conversions, such as 1 km = 1000 m or 1 inch = 2.54 cm, as they are frequently used. Being proficient at unit conversion can prevent errors in calculations and is a valuable skill in not only physics but in various scientific and engineering fields.