SUMMARY
The discussion focuses on calculating the height a dart reaches when shot from a spring-loaded dart gun, specifically when the spring is compressed half as far compared to a previous shot that achieved a height of 24 meters. Using the formula for elastic potential energy (EPE = 0.5kx²) and gravitational potential energy (GPE = mgh), it is established that compressing the spring to half its original distance results in a reduction of potential energy to one-fourth, leading to a maximum height of 6 meters for the second shot. This conclusion is derived from the direct proportionality between the potential energy stored in the spring and the height achieved by the dart.
PREREQUISITES
- Understanding of Hooke's Law and spring mechanics
- Knowledge of gravitational potential energy calculations
- Familiarity with energy conservation principles
- Basic algebra for manipulating equations
NEXT STEPS
- Study the relationship between elastic potential energy and gravitational potential energy
- Learn about the implications of Hooke's Law in real-world applications
- Explore more complex spring systems and their energy transformations
- Investigate the effects of friction and air resistance on projectile motion
USEFUL FOR
Students studying physics, particularly those focusing on mechanics and energy conservation, as well as educators looking for practical examples of spring dynamics and energy transfer concepts.