Spring and Incline Plane (Conservation of Energy Problem)

[jzwiep]

Homework Statement

MP: 10.71
A 25 kg box slides 4.0 m down the frictionless ramp shown in the figure , then collides with a spring whose spring constant is 250 N/m.

What is the maximum compression of the spring? ds=2.5m
For what compression of the spring does the box have the maximum speed? ds=??

Homework Equations

Energy is conserved.

Ei = Ef

The Attempt at a Solution

Potential at top of the ramp = Spring potential at ds max

ds=mg/2k(1+sqrt((1+4Lk)/mg)

Which got me the correct answer to the first question
For the second question I tried:

Potential at top of ramp = Kinetic at top of spring = Spring Potential

but I couldn't get a workable solution.

Intuitively I thought the answer would be ds=0, but it wasn't.

Any thoughts?

 

[Doc Al]

Consider the net force on the box as it goes through its motion. As long as the net force is down the ramp it will continue to accelerate.

 

[jzwiep]

Consider the net force on the box as it goes through its motion. As long as the net force is down the ramp it will continue to accelerate.

Ah, that did it. I wonder though. When I asked my TA if I could find the ds with Spring Force=Gravitational Force, he said that the final spring compression would be different for an object that is accelerating into the spring versus one that is just in static equilibrium, and that I couldn't use it in this situation. Did his point have any validity?

 

[tiny-tim]

welcome to pf!

hi jzwiep! welcome to pf!

yes, Spring Force=Gravitational Force only gives you zero acceleration, not zero velocity (except in static equilibrium, when of course they're the same)

 

[Doc Al]

Ah, that did it. I wonder though. When I asked my TA if I could find the ds with Spring Force=Gravitational Force, he said that the final spring compression would be different for an object that is accelerating into the spring versus one that is just in static equilibrium, and that I couldn't use it in this situation. Did his point have any validity?

Realize that you are solving for two different spring compressions. We are discussing the second one: The compression where speed is maximum. His comments apply to the first question (finding the final or maximum compression), not to the second one.