Calculating height using energy | Modeling Energy | High School Physics | Khan Academy

TL;DR

The maximum height of a ball launched by a compressed spring can be determined using the principle of conservation of energy.

Transcript

• [Instructor] So I have an uncompressed spring here and the spring has a spring constant of four Newtons per meter. Then I take a 10 gram mass, a 10 gram ball, and I put it at the top of the spring and I push down to compress that spring by 10 centimeters. And so let's call that scenario one right over there, where our mass is on top of this compr... Read More

Key Insights

• 💬 Conservation of energy is a fundamental principle that can be applied to determine the maximum height of a ball launched by a compressed spring.
• ❓ The scenario involves both gravitational potential energy and elastic potential energy.
• 🥵 Ignoring factors such as heat due to friction with the air can simplify the problem.

Questions & Answers

Q: How can the maximum height of a ball launched by a compressed spring be determined?

The maximum height can be determined by applying the principle of conservation of energy, ensuring that the potential energy and kinetic energy in the initial scenario are equal to the potential energy and kinetic energy at maximum height.

Q: What are the types of potential energy involved in the scenario?

The scenario involves gravitational potential energy and elastic potential energy due to the compressed spring.

Q: Why is heat due to friction with the air ignored in this analysis?

Heat due to friction is ignored in order to simplify the problem. The analysis assumes the scenario is happening in a vacuum.

Q: How is the maximum height calculated using the conservation of energy principle?

The maximum height can be calculated by dividing the elastic potential energy in scenario one by the product of mass, gravitational field strength, and the spring constant, all multiplied by the compressed distance squared.

Summary & Key Takeaways

• The content discusses a scenario where a mass is placed on top of a compressed spring and then launched into the air, reaching a maximum height.

• The principle of conservation of energy is applied to determine the maximum height.

• The potential energy and kinetic energy in the initial scenario must be equal to the potential energy and kinetic energy in the scenario of maximum height.