AP Physics Questions on Escape Velocity with Explanations

🚀 Quick Study Guide

• 🌌 Definition: Escape velocity is the minimum speed needed for an object to escape the gravitational influence of a massive body. Think of it as the speed required to leave a planet without further propulsion.
• 🍎 Formula: The escape velocity ($v_e$) from a body of mass $M$ and radius $r$ is given by: $v_e = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant ($6.674 × 10^{-11} N(m/kg)^2$).
• 📏 Key Factors: Escape velocity depends only on the mass and radius of the body you're escaping from, not on the mass of the object trying to escape.
• 💡 Important Note: The direction of the initial velocity doesn't matter, as long as the object achieves the minimum speed. We usually consider launching straight up for simplicity.
• 🌍 Earth's Escape Velocity: Approximately 11.2 km/s. This is the speed you'd need to launch a rocket to escape Earth's gravity.

🧪 Practice Quiz

1. What is the escape velocity from a planet with mass $M$ and radius $r$?
   1. $v_e = \sqrt{\frac{GM}{r}}$
   2. $v_e = \frac{GM}{r}$
   3. $v_e = \sqrt{\frac{2GM}{r}}$
   4. $v_e = \frac{2GM}{r}$
2. How does the mass of the escaping object affect the escape velocity?
   1. The escape velocity increases with the mass of the escaping object.
   2. The escape velocity decreases with the mass of the escaping object.
   3. The escape velocity is not affected by the mass of the escaping object.
   4. The escape velocity is directly proportional to the square of the mass of the escaping object.
3. If the radius of a planet is doubled, and the mass remains the same, what happens to the escape velocity?
   1. It doubles.
   2. It halves.
   3. It increases by a factor of $\sqrt{2}$.
   4. It decreases by a factor of $\sqrt{2}$.
4. Planet X has twice the mass and twice the radius of Earth. What is the escape velocity of Planet X compared to Earth?
   1. The same.
   2. Twice as much.
   3. Half as much.
   4. Four times as much.
5. Which of the following is NOT a factor in determining escape velocity?
   1. Mass of the planet.
   2. Radius of the planet.
   3. Gravitational constant.
   4. Mass of the escaping object.
6. If a rocket achieves a speed greater than the escape velocity, what will happen?
   1. It will enter a stable orbit.
   2. It will fall back to the planet's surface.
   3. It will escape the planet's gravitational pull and continue into space.
   4. It will explode.
7. What is the approximate escape velocity from Earth?
   1. 1.12 km/s
   2. 11.2 km/s
   3. 112 km/s
   4. 1120 km/s