Spring Constant when compressed

AI Thread Summary
To determine the spring constant for a 6kg block sliding down a frictionless ramp and compressing a spring by 45 cm, energy conservation principles are applied. The gravitational potential energy (PEg) at the top of the ramp is calculated as 58.8 J. This energy is converted into elastic potential energy (PEs) when the spring is compressed. By equating the two forms of energy, the spring constant can be derived. The approach of using energy conservation is confirmed as correct for solving the problem.
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Homework Statement



A 6kg block is released from the top of a 1.0m ramp (frictionless) and slides into a horizontal spring, compressing it 45 cm. Determine the spring constant.



Homework Equations



PEg = mgh (6*9.8*1) = 58.8

PEs = 1/2kx^2 (1/2*k*.45^2)



The Attempt at a Solution



Do I set the two equations equal to each other and get 582.2 as the spring constant?
 
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Yeah that seems like the right approach to use: energy conservation. All of the gravitational PE that the object had at the top of the ramp is converted into KE by the time it reaches the bottom of the ramp, and then into elastic PE as it compresses the spring. So assuming no losses due to friction, you can equate the initial and final PE.
 

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