Spring constant of mass-less spring

[alfredo24pr]

Homework Statement

A "mass less" spring has a length of 0.350 m in its relaxed position. It is compressed to 70.0 percent of its relaxed length, and a mass M= 0.150 kg is placed on top and released from rest. Find the spring constant

Homework Equations

mgh=1/2kx2

The Attempt at a Solution

mgh=1/2kx2

2mgh/x2=k

k = 2(0.150)(9.8)(0.350) / 0.105(sqrd)

the 0.105 comes from (0.350 - 70% of 0.350)

Am I doing something wrong?

 

[Doc Al]

A "mass less" spring has a length of 0.350 m in its relaxed position. It is compressed to 70.0 percent of its relaxed length, and a mass M= 0.150 kg is placed on top and released from rest. Find the spring constant

Are you sure this is an accurate statement of the problem? There doesn't seem to be enough information to find the spring constant. (The same conditions can apply to any spring constant.)

Make sure you've presented the problem exactly as given to you, word for word.

 

[alfredo24pr]

Are you sure this is an accurate statement of the problem? There doesn't seem to be enough information to find the spring constant. (The same conditions can apply to any spring constant.)

Make sure you've presented the problem exactly as given to you, word for word.

Oops! I forgot the last sentence! Sorry

The mass then travels vertically and it takes 1.50 s for the mass to reach the top of its trajectory. Calculate the spring constant, in N/m. (Use g=9.81 m/s2). Assume that the time required for the spring to reach its full extension is negligible.

 

[Doc Al]

Am I doing something wrong?

You haven't made use of the 1.5 second time. That should give you a clue where you might have missed something.

Also: Your use of mgh=1/2kx^2 ignores the kinetic energy that the mass has once the spring uncompresses.

 

[alfredo24pr]

You haven't made use of the 1.5 second time. That should give you a clue where you might have missed something.

Also: Your use of mgh=1/2kx^2 ignores the kinetic energy that the mass has once the spring uncompresses.

Oh, so I was thinking:

mgh + 1/2mv(sqrd) = 1/2kx(sqrd)

Is that correct?

 

[Doc Al]

Oh, so I was thinking:

mgh + 1/2mv(sqrd) = 1/2kx(sqrd)

Is that correct?

Sounds good. Use the time to figure out the speed.

 

[alfredo24pr]

Sounds good. Use the time to figure out the speed.

ok! Thank you a lot :)

 

[alfredo24pr]

Sounds good. Use the time to figure out the speed.

Im not getting the answer

1/2kx2 = mgh + 1/2mv2

1/2k (0.245)2 = (.150)(9.8)(0.105) + 1/2 (0.150)[(0.245/1.5)]2

0.0300125 k = 0.15435 + 0.002001

0.0300125 k = 0.1563508

k = 5.209 N/m

this does not give me the answer?

 

[SammyS]

[STRIKE]This is a case of Simple Harmonic Motion. Do you know how the period of the motion is related to the mass and the spring constant?[/STRIKE]

Ignore this post! DUH !

 

[Doc Al]

Im not getting the answer

1/2kx2 = mgh + 1/2mv2

1/2k (0.245)2 = (.150)(9.8)(0.105) + 1/2 (0.150)[(0.245/1.5)]2

How did you figure out the speed? (Hint: Once the mass leaves the spring, it's a projectile.)

 

[alfredo24pr]

How did you figure out the speed? (Hint: Once the mass leaves the spring, it's a projectile.)

So, every other thing is correct? it is just the speed?

I have to use: y = y_o + v_oyt - 1/2gt²?

 

[Doc Al]

So, every other thing is correct? it is just the speed?

Not exactly:

1/2k (0.245)2 = (.150)(9.8)(0.105) + 1/2 (0.150)[(0.245/1.5)]2

How did you get that displacement?

I have to use: y = y_o + v_oyt - 1/2gt²?

You don't have the distance. But you can directly relate speed and time.

 

[alfredo24pr]

Not exactly:

​

How did you get that displacement?

You don't have the distance. But you can directly relate speed and time.

ok.. so,

1/2kx² = 1/2k (0.350)² right?

I really do not understand how to get the speed. Obviously the time is 1.5s, but what displacement do I use?

 

[Doc Al]

ok.. so,

1/2kx² = 1/2k (0.350)² right?

No. How much is the spring compressed? (You had this figured out in your first post.)

I really do not understand how to get the speed. Obviously the time is 1.5s, but what displacement do I use?

You don't need displacement. How are velocity, acceleration, and time related?

 

[alfredo24pr]

No. How much is the spring compressed? (You had this figured out in your first post.)


You don't need displacement. How are velocity, acceleration, and time related?

x=0.105m

and for the velocity:

v = v_o +gt

v = 0 + 9.8(1.5) = 14.7 m/s

I got the answer now! Thank you for your patience!