Law of Conservation of Energy Question

[kylepetten]

Homework Statement

A 10.0 kg mass slides from rest down a frictionless inclined plane from a height of 0.500 m. After traveling 5.0 m along the ramp, it moves along a horizontal surface (frictionless again) where it makes contact with a spring. The force constant of the spring is 100.0 N/m. Determine the distance that the spring is compressed before the mass comes momentarily to a halt.

m=10.0 kg
k=100.0 N/m
h=0.500 m

Homework Equations

KE (initial) + PE (initial) = KE (final) + PE (final)

The Attempt at a Solution

{Initial} [1/2(m)(v^2)]+[1/2(k)(x^2)] = {Final} [1/2(m)(v^2)]+[1/2(k)(x^2)]

That's all I could do. I do not know if I have the correct equation here. But, if I do, I do not know how to get the (v^2) in the equation.

Also, another thing that is troubling me is that I do not know what effect the incline has on the question, or if it does at all.

Thanks, in advance, for your help!

 

[rl.bhat]

Here the inclined plane is used to accelerate the mass.
Find
KE (initial) + PE (initial) = KE (final) + PE (final). That will give you the final KE of the mass when it starts moving on the horizontal surface.
Again using the conservation of energy, you find the compression in the spring.

 

[Doc Al]

I do not know if I have the correct equation here.

You forgot about gravitational PE.

But, if I do, I do not know how to get the (v^2) in the equation.

Take your initial point to be when the mass is first released (what's its speed then?) and the final point to be when the spring is maximally compressed (what's its speed then?).

 

[Stonebridge]

It's the height of the mass at the start that matters. That's 0.500m
Work out the PE. This is converted totally to KE as it slides down the frictionless track.
There is no need to find its velocity, though!
All this KE is then converted into the elastic PE in the spring.

 

[holezch]

the block starts from rest (so it is not moving), then it has no kinetic energy, but it has gravitational potential energy. as it falls down , it gains kinetic energy, but since the total mechanical energy is conserved in this system, the gravitational potential energy starts reducing at the same rate (same as the gain of kinetic energy). Also, it loses gravitational potential energy simply because it is falling down. Then, it gains potential energy again as it gets in contact with the spring

 

[kylepetten]

You forgot about gravitational PE.

Take your initial point to be when the mass is first released (what's its speed then?) and the final point to be when the spring is maximally compressed (what's its speed then?).

It's the height of the mass at the start that matters. That's 0.500m
Work out the PE. This is converted totally to KE as it slides down the frictionless track.
There is no need to find its velocity, though!
All this KE is then converted into the elastic PE in the spring.

the block starts from rest (so it is not moving), then it has no kinetic energy, but it has gravitational potential energy. as it falls down , it gains kinetic energy, but since the total mechanical energy is conserved in this system, the gravitational potential energy starts reducing at the same rate (same as the gain of kinetic energy). Also, it loses gravitational potential energy simply because it is falling down. Then, it gains potential energy again as it gets in contact with the spring

So, how about this:

[0] + [(10 kg)(9.8)(0.5 m)] = [1/2(10 kg)(0^2)] = [1/2(100 N/m)(x^2)]
0 + 49 = 0 + [50(x^2)]
x= {sqrt[49/50]}
x= 0.99m

Did I do this right?

Thanks for all the replies by the way!

 

[Doc Al]

Did I do this right?

Yes. Perfect!

 

[kylepetten]

Yes. Perfect!

Thanks very very much!