AP Physics 1: Gravitational Potential Energy multiple choice questions

📚 Quick Study Guide

• 🌍 Definition: Gravitational Potential Energy (GPE) is the energy an object possesses due to its position in a gravitational field.
• 📏 Formula: GPE is calculated using the formula $U = mgh$, where:
  • $U$ = Gravitational Potential Energy (in Joules)
  • $m$ = mass (in kg)
  • $g$ = acceleration due to gravity (approximately $9.8 m/s^2$ on Earth)
  • $h$ = height above a reference point (in meters)
• 📍 Reference Point: The choice of the reference point (where $h = 0$) is arbitrary, but it's crucial to be consistent throughout a problem.
• 🔄 Work-Energy Theorem: The change in GPE is equal to the negative of the work done by the gravitational force: $\Delta U = -W_g$
• 💡 Key Concept: GPE is a scalar quantity, meaning it has magnitude but no direction.
• 🤔 Important Note: When an object moves upward against gravity, its GPE increases. When it moves downward, its GPE decreases.

🧪 Practice Quiz

1. A 2 kg ball is held 3 meters above the ground. What is its gravitational potential energy relative to the ground?
   1. 6 J
   2. 19.6 J
   3. 58.8 J
   4. 29.4 J
2. A 5 kg block is lifted vertically at a constant speed of 2 m/s to a height of 4 meters. What is the change in its gravitational potential energy?
   1. 20 J
   2. 40 J
   3. 100 J
   4. 196 J
3. A roller coaster car with a mass of 1000 kg is at the top of a hill that is 50 meters high. What is the gravitational potential energy of the car at the top of the hill relative to the bottom?
   1. 5,000 J
   2. 49,000 J
   3. 98,000 J
   4. 490,000 J
4. If the height of an object is doubled, what happens to its gravitational potential energy?
   1. It is halved.
   2. It remains the same.
   3. It doubles.
   4. It quadruples.
5. A 3 kg book falls from a shelf that is 1.5 meters high. What is the change in gravitational potential energy of the book as it falls to the floor? (Assume the floor is the zero reference point.)
   1. -44.1 J
   2. 44.1 J
   3. -22.05 J
   4. 22.05 J
6. A spring with a force constant $k$ is stretched a distance $x$. Which of the following represents the gravitational potential energy?
   1. $\frac{1}{2}kx^2$
   2. $mgh$
   3. $\frac{1}{2}mv^2$
   4. $kx$
7. Two objects have the same gravitational potential energy. Object A has twice the mass of Object B. How do their heights compare, assuming the same 'g'?
   1. Object A is twice as high as Object B.
   2. Object B is twice as high as Object A.
   3. They are at the same height.
   4. Object A is four times as high as Object B.