Solving Homework Equations for Speed

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SUMMARY

The discussion focuses on solving two physics problems involving energy conservation. The first problem involves an 85 g wooden block compressed against a spring with a spring constant (k) of 78 N/m, where the speed at the initial point is derived from potential energy stored in the spring. The second problem examines a 5.0 kg crate sliding down a ramp at a 38-degree angle, where the speed at the bottom can be calculated using gravitational potential energy. Both problems utilize the equations for elastic potential energy (Us), gravitational potential energy (Ug), and kinetic energy (KE).

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with elastic potential energy (Us = 0.5kx²)
  • Knowledge of gravitational potential energy (Ug = mgh)
  • Ability to apply kinetic energy formula (KE = 0.5mv²)
NEXT STEPS
  • Calculate the speed of the wooden block using energy conservation principles
  • Analyze the effects of ramp angle on the speed of the crate
  • Explore the relationship between spring constant and energy stored
  • Investigate real-world applications of energy conservation in mechanical systems
USEFUL FOR

Students studying physics, educators teaching energy conservation concepts, and anyone interested in solving mechanics problems involving springs and inclined planes.

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Homework Statement


1. An 85 g wooden block is set up against a spring. The block is pushed into the spring, compressing it a distance of 2.0cm and then released. k= 78N/m. What is the speed of the block when it reaches its initial point.

2. A 5.0kg crate slides down a smooth ramp that is elevated at an angle of 38 degrees. length of ramp= 2m. What will be the speed of the crate at the bottom of the ramp?


Homework Equations


Us= .5kx^2
Ug= mgh
KE=.5mv^2

The Attempt at a Solution


1. Us= .0156J? I don't know how to find its speed.

Any help you can provide is appreciated. Thanks in advance.
 
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The solution to both questions lie in the idea of conservation of energy.
 

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