91Ó°ÊÓ

Work done by gravity is essentially the energy transferred to an object by the force of gravity as it moves between two points. To put it simply, it measures how much force gravity exerts on the object as it changes height. Gravity does the work whenever an object moves vertically along the direction of the force of gravity.

To calculate the work done by gravity, we use the formula:

• \( W = mgh \)

where:

• \( W \) is the work done by gravity
• \( m \) is the mass of the object
• \( g \) is the acceleration due to gravity (approximately \( 9.81\, m/s^2 \) on Earth)
• \( h \) is the height change the object undergoes

In the context of our basketball, as it falls from 6.1 m to 1.5 m above ground, gravity exerts a force throughout this height change. The work done by gravity converts potential energy at the starting height to kinetic energy and back to potential energy at the ending height. The formula showcases gravity’s role in energy transformation.

The principle of energy conservation is fundamental in physics, emphasizing that energy cannot be created or destroyed. It can only change forms. This is seen in the transition between potential and kinetic energy.

In the basketball example:

• The basketball possesses potential energy due to its height.
• As it falls, this potential energy converts into kinetic energy (energy of motion).
• When the ball is caught, it again holds potential energy, but less than initially because it's closer to the ground.

The energy remains constant throughout, only its form changes. When the basketball drops:

• Initial energy (when released) = gravitational potential energy
• Midway during the fall = mix of potential and kinetic energy
• Just before being caught = kinetic energy

Thus, the law of conservation of energy at play shows us how gravitational forces seamlessly exchange energy forms without losing any total energy in the isolated system of the ball and Earth.

Calculating gravitational potential energy is like determining the stored energy an object possesses due to its position in a gravitational field. It’s energy held thanks to height above a reference point, typically the ground.

The formula used is:

• \( PE = mgh \)

where:

• \( PE \) stands for potential energy
• \( m \) is the object's mass
• \( g \) is the acceleration from gravity
• \( h \) measures how high the object is from the reference point

Applying it to the basketball scenario:

• When released from 6.1m, potential energy is calculated using \( PE_0 = 0.60 \times 9.81 \times 6.1 \).
• When caught at 1.5m, it transforms to \( PE_f = 0.60 \times 9.81 \times 1.5 \).

This calculation reinforces the understanding of how height impacts stored gravitational energy. As the basketball falls to a lower height, its potential energy decreases, validating the role height plays in the energy retention of a lifting or falling mass.