For Problem #4, assume the maximum compression of the spring is
“Xmax”. When defining the energy stored in the spring, you should
write it in terms of Xmax so that Us = (1/2)k (Xmax-x)^2. That way,
x can be the location of the mass along the ramp, with x=0 at its
lowest possible spot, x=Xmax where the spring is not compressed,
but the mass is in contact with it, and x> Xmax has the mass
located somewhere on the ramp above the spring. I’ll leave it to
you to calculate where the mass is located when the problem first
starts.
4. A 20.0 kg box initially at rest, slides 4.0 m down a frictionless ramp, and then collides with a spring whose spring constant a. What is the maximum compression of b. At what compression of the spring is 250 N/m. The ramp incline is 30°. 4.0 m the spring? does the mass have its maximum 30° SE?
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