Solving AP Physics: Spring Compression Problem

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SUMMARY

The discussion focuses on solving a spring compression problem involving a 20 kg mass sliding down a frictionless incline at a 30-degree angle, impacting a spring with a spring constant of 200 N/m. The participant successfully calculated the speed of the block just before it hits the spring as 7.75 m/s using the kinematic equation V² = Vo² + 2ad. However, they encountered difficulties in determining the height for calculating the potential energy and spring compression, indicating a need for a clearer understanding of the relationship between spring compression and height using trigonometric principles.

PREREQUISITES
  • Understanding of kinematic equations, specifically V² = Vo² + 2ad
  • Knowledge of potential energy (PE) and kinetic energy (KE) concepts
  • Familiarity with spring potential energy formula PE spring = 1/2kx²
  • Basic trigonometry to relate spring compression and height
NEXT STEPS
  • Study the derivation and application of the kinematic equation V² = Vo² + 2ad in inclined plane problems
  • Learn how to calculate gravitational potential energy (PE = mgh) in relation to height and incline angles
  • Explore the relationship between spring compression and height using trigonometric functions
  • Review conservation of mechanical energy principles in spring-mass systems
USEFUL FOR

Students studying AP Physics, particularly those focusing on mechanics involving inclined planes and spring systems, as well as educators seeking to clarify concepts of energy conservation and kinematics.

devolg632104
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Homework Statement



A 20 kg mass released from rest slides down a frictionless plane inclined at an angle of 30 deg with the horizontal and strikes a spring of spring constant K=200 Newtons/meter. Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is conserved. Use g = 10 m/s^2.

a. Determine the speed of the block just before it hits the spring.
b. Determine the distance the spring has been compressed when the block comes to rest.
c. Determine the distance the spring is compressed when the block reaches maximum speed.

Homework Equations



a. V^2=Vo^2 +2ad
b. PE spring = 1/2kx^2
PE = mgh
KE = 1/2mv^2
PE +KE = PE spring
c. Totally clueless


The Attempt at a Solution


For part a, I found what the force of gravity was in the x direction, divided by the mass, and then found the acceleration. Then I plugged that and the given variables into the kinematic equation

V^2=Vo^2 +2ad

And the answer I got was 7.75 m/s

For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.

Thanks for the help!
 
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devolg632104 said:
For part b, I tried Ug+K=Us, but I cannot determine the height so I do not know how to do this.
The amount of spring compression and the change in height are related by a little trig.
 

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