What is the distance the spring is compressed ...physics help ?

K

Kelly

New member
A 500-g block is released from rest and slides down a frictionless track that begins 2.60 m above the horizontal, as shown in the figure below. At the bottom of the track, where the surface is horizontal, the block strikes and sticks to a light spring with a spring constant of 25.0 N/m.

Find the maximum distance the spring is compressed.
 
The principle is that the kinetic energy of the block at the bottom of the track is equal to the kinetic energy of the block at the bottom. Which in turn is equal to the potential energy of the spring. Combining these the potential of the block at the top of the track is equal to the potential stored in the spring when it is fully compressed.

mgh=.5kx^2
(.5)(9.8)(2.6)=.5(25)x^2
x^2=1.01
x= 1.00 meters
the spring compresses a maximum of 1 meter
 
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