Use this diagram and scenario to answer all the essay questions that follow:

The basketball in the diagram is thrown from point A, travels up to
point C, and then hits the ground at point E. Changes in the ball’s
kinetic and potential energy are happening each moment.
A) 11. Calculate the potential energy at point C. The ball’s mass is 200 grams. Point C is 8
meters above ground zero. Make sure to show your work and include units. (Earth’s
acceleration due to gravity is 9.8 m/s2)

1 answer

To calculate the potential energy (PE) at point C, we can use the formula for gravitational potential energy:

\[ \text{PE} = m \cdot g \cdot h \]

where:

  • \( m \) is the mass of the object in kilograms (kg)
  • \( g \) is the acceleration due to gravity in meters per second squared (m/s²)
  • \( h \) is the height above the ground in meters (m)

Given:

  • Mass of the ball (\( m \)) = 200 grams = 0.200 kg (since 1 kg = 1000 grams)
  • Height at point C (\( h \)) = 8 meters
  • Acceleration due to gravity (\( g \)) = 9.8 m/s²

Step-by-step calculation:

  1. Convert the mass to kg: \( 200 \text{ grams} = \frac{200}{1000} = 0.200 \text{ kg} \)

  2. Plug the values into the formula: \[ \text{PE} = 0.200 , \text{kg} \cdot 9.8 , \text{m/s}^2 \cdot 8 , \text{m} \]

  3. Calculate the potential energy: \[ \text{PE} = 0.200 \cdot 9.8 \cdot 8 \] \[ \text{PE} = 0.200 \cdot 78.4 \] \[ \text{PE} = 15.68 , \text{Joules} \]

Conclusion:

The potential energy at point C is 15.68 Joules.