Solved Examples of Gravitational Potential Energy Problems

📚 Quick Study Guide

• 🌍 Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field.
• 📏 The formula for GPE is: $GPE = mgh$, where:
  • $m$ = mass of the object (in kg)
  • $g$ = acceleration due to gravity (approximately $9.8 m/s^2$ on Earth)
  • $h$ = height of the object above a reference point (in meters)
• ⚖️ The reference point (where GPE is zero) is arbitrary but usually chosen as the ground or the lowest point in the problem.
• 💡 GPE is a scalar quantity, meaning it has magnitude but no direction.
• 📝 The change in GPE ($\Delta GPE$) is often more important than the absolute value of GPE, especially when dealing with work and energy conservation.

🧪 Practice Quiz

1. A 2 kg book is held 1.5 meters above the floor. What is its gravitational potential energy relative to the floor? (Assume $g = 9.8 m/s^2$)
   1. 29.4 J
   2. 3.0 J
   3. 14.7 J
   4. 0 J
2. A 0.5 kg ball is dropped from a height of 10 meters. What is its gravitational potential energy just before it is released? (Assume $g = 9.8 m/s^2$)
   1. 49 J
   2. 5 J
   3. 9.8 J
   4. 0 J
3. An object has a gravitational potential energy of 98 J at a height of 10 meters. What is its mass? (Assume $g = 9.8 m/s^2$)
   1. 1 kg
   2. 10 kg
   3. 0.1 kg
   4. 9.8 kg
4. A 5 kg block is lifted from the ground to a height of 3 meters. How much work is done against gravity? (Assume $g = 9.8 m/s^2$)
   1. 147 J
   2. 15 J
   3. 49 J
   4. 0 J
5. A roller coaster car with a mass of 500 kg is at the top of a hill that is 30 meters high. What is its gravitational potential energy relative to the bottom of the hill? (Assume $g = 9.8 m/s^2$)
   1. 147,000 J
   2. 15,000 J
   3. 1633.33 J
   4. 0 J
6. If the gravitational potential energy of a 2 kg object increases by 50 J as it is lifted, by how much was its height increased? (Assume $g = 9.8 m/s^2$)
   1. 2.55 m
   2. 5 m
   3. 10 m
   4. 0.2 m
7. A 3 kg ball is initially at a height of 5 meters and then rolls down to a height of 2 meters. What is the change in its gravitational potential energy? (Assume $g = 9.8 m/s^2$)
   1. -88.2 J
   2. 88.2 J
   3. 29.4 J
   4. -29.4 J