SUMMARY
The speed of a rubber dart, with a mass of 7.8 grams, as it leaves a toy is calculated using the principles of energy conservation. The dart is propelled by a spring with a force constant of 350 N/m, initially compressed by 4.5 cm. The elastic potential energy stored in the spring is entirely converted into kinetic energy of the dart. The final speed of the dart can be determined using the equations Ee = Ek and Ee = 1/2 k x^2, leading to a definitive calculation of its exit velocity.
PREREQUISITES
- Understanding of energy conservation principles
- Familiarity with Hooke's Law and spring constants
- Knowledge of kinetic energy equations
- Basic algebra for solving equations
NEXT STEPS
- Calculate the speed of the dart using the formula v = sqrt((k * x^2) / m)
- Explore the effects of varying spring constants on projectile speed
- Investigate energy loss factors in real-world applications of spring-powered toys
- Learn about the relationship between mass and velocity in projectile motion
USEFUL FOR
Students studying physics, educators teaching mechanics, and hobbyists interested in the physics of toy projectiles will benefit from this discussion.