Understanding Potential Energy

Potential energy is the energy an object possesses due to its position or state. For an object elevated above a reference point (like the ground), this is called gravitational potential energy. It depends on the object's mass, the acceleration due to gravity, and the height above the reference point.

Calculating Gravitational Potential Energy

The formula for gravitational potential energy (PE) is:

\(PE = mgh\)

Where:

• \(m\) is the mass of the object
• \(g\) is the acceleration due to gravity
• \(h\) is the height above the reference point

Applying the Potential Energy Formula

Let's identify the given values in the question about the 100 gram ball on top of a 70 m building:

• Mass of the ball, \(m = 100 \, \text{grams}\)
• Height of the building, \(h = 70 \, \text{m}\)
• Acceleration due to gravity, \(g = 10 \, \text{m/s}^2\)

Before calculating, we need to ensure all units are consistent with the standard SI units. Mass is given in grams, so we convert it to kilograms:

\(100 \, \text{grams} = \frac{100}{1000} \, \text{kg} = 0.1 \, \text{kg}\)

Now, we can substitute the values into the potential energy formula:

\(PE = (0.1 \, \text{kg}) \times (10 \, \text{m/s}^2) \times (70 \, \text{m})\)

Let's perform the calculation step-by-step:

\(PE = (0.1 \times 10) \, \text{kg} \cdot \text{m/s}^2 \times 70 \, \text{m}\)

\(PE = 1 \, \text{N} \times 70 \, \text{m}\) (Since \(1 \, \text{kg} \cdot \text{m/s}^2 = 1 \, \text{Newton, N})\)

\(PE = 70 \, \text{J}\) (Since \(1 \, \text{N} \cdot \text{m} = 1 \, \text{Joule, J})\)

So, the potential energy of the ball at the top of the 70 m building is 70 Joules.

Conclusion on Potential Energy

By using the formula \(PE = mgh\) and converting the mass to kilograms, we found that the gravitational potential energy of the 100 gram ball at a height of 70 meters, with \(g = 10 \, \text{m/s}^2\), is 70 J.

Revision Table: Key Concepts for Potential Energy

Additional Information on Potential Energy and Energy Forms

Potential energy is one of the fundamental forms of energy. Energy can exist in various forms and can be transformed from one form to another.

• Other Forms of Potential Energy: Besides gravitational potential energy, there is elastic potential energy (stored in stretched or compressed springs) and chemical potential energy (stored in chemical bonds).
• Kinetic Energy: This is the energy of motion. An object in motion has kinetic energy, given by \(KE = \frac{1}{2}mv^2\), where \(m\) is mass and \(v\) is velocity.
• Conservation of Energy: In a closed system without external forces like friction, the total mechanical energy (sum of potential energy and kinetic energy) remains constant. As the ball falls from the building, its potential energy decreases, but its kinetic energy increases, such that their sum stays the same.
• Work and Energy: Work done on an object changes its energy. If work is done against gravity to lift an object, its gravitational potential energy increases.