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Understanding PE in a Dart Gun and Spring Ejection System

Learn about the physics of Potential Energy in dart guns and spring systems. Explore concepts of PE elastic, spring properties, and Hooke's Law with practical examples and calculations. Discover how PE impacts scenarios like a spring-powered ejection mechanism in a thrilling story.

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Understanding PE in a Dart Gun and Spring Ejection System

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  1. PE of a A New Kind of Potential: Elastic PE

  2. Consider a toy gun… Ohh… A DART gun! • What makes the dart shoot out? Where does the Kinetic Energy come from??

  3. PE of a Spring • The Potential Energy (PEelastic) of a spring is described by:

  4. PE of a Spring • k is the spring constant. Its different for every spring. (N/m) • x is the displacement of the spring. How much its stretched or squished… (m)

  5. Spring Properties • As you pull a spring, it gets harder to pull the farther you go. • This is equally true if you try to compress it from it’s resting state. • The amount of Forceneeded to stretch OR compress a spring is shown by Hooke’s Law:

  6. An Example: • A spring hanging vertically measures 0.3m. When a 1kg weight is attached, the spring stretches to a length of 0.8m. Determine the spring constant.

  7. Another Example: • A spring of spring constant k= 50 N/m is compressed 50cm. How fast will it shoot a 0.010kg dart when released?

  8. Putting it all together • James Bond (80kg) is driving at 80m/s in his Prius when he goes off a 100m cliff. His spring ejection mechanism has a spring constant of k=500 N/m and has been compressed 2m to fit in the car. Unfortunately his parachute fails… How fast is Mr. Bond going to hit the ground?

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