Physics--Spring constant problems

[SouthernDoc2Be]

Hey yall--I'm reviewing spring constants and want to check my answers to the following questions:

A block of mass m is released on a frictionless ramp with a spring of spring constant K below. You are to use energy as in E=1/2kx^2.

a) How fast is the block going when it exits the ramp?
b) How far is the spring compressed?
3) How high will the block slide by the ramp after the spring pushes the block away.

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[Cawolf]

If you want to check your answers, post your answers.

 

[SouthernDoc2Be]

a) 10 m/s
b) mgh=1/2kx^2--what do I use for height as no distance is given
c) I do not know how to do this.

 

[Cawolf]

a) Without height I don't know how you obtained this number. It should just derive to v = sqrt(2gh).

b) You know the PE of the block is mgh, so set that equal to the spring equation and solve to get x = sqrt(2mgh/k)

c) If energy is conserved and the spring is ideal with no friction. . .

 

[SouthernDoc2Be]

Well, I thought for a) since nothing was given, and it is sliding down, that acceleration would be equal to the velocity. So I didn't use height to get that answer, which is why I am stumped on B.

 

[Cawolf]

Acceleration cannot be equal to velocity, they are different quantities (check your units). Set the PE and KE formulas equal to each other and see that if PE = KE, then mgh = 0.5mv^2. Mass cancels and you can see that the velocity is height dependent. You need to know how long the object accelerated to know a velocity.

If height is not given, assume that it is h.

 

[SouthernDoc2Be]

Back to the drawing board I go. Thanks for your help.