Spring Constant Question: Need Help

[Paymemoney]

Spring Constant Question:URGENT Need Help!

Hi

I am having trouble with this question can someone solve it for me, I have a test tomorrow i really need to get this done.

Homework Statement

A person building a seismograph (for detecting earthquakes) needs a heavy mass suspended by a long spring. He constructs the long spring from 8 identical short springs connected together end to end( in series). He attaches one end of this long spring to the roof and hangs a 10.25 kg mass from it. The resonant frequency of this system is exactly 1.26Hz

a) What is the spring constant of this long spring?

b) What is the long spring extension when the mass is attached to it?

c) What is the spring constant of each short spring?

Homework Equations

F=-kx

$$T=2\pi\sqrt{\frac{m}{k}}$$

The Attempt at a Solution

a) 642.429

b) not sure

c) i tried to use the $$\frac{1}{k_t} = \frac{1}{k_1} + \frac{1}{k_2}$$

P.S

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Redbelly98]

The Attempt at a Solution

a) 642.429

b) not sure

c) i tried to use the $$\frac{1}{k_t} = \frac{1}{k_1} + \frac{1}{k_2}$$

(a) Looks good.
(b) The F=-kx equation is helpful here. Hint: F is the weight of the mass.
(c) That approach should work. Of course, there are 8 individual springs, not just 2.

 

[Paymemoney]

(a) Looks good.
(b) The F=-kx equation is helpful here. Hint: F is the weight of the mass.
(c) That approach should work. Of course, there are 8 individual springs, not just 2.

b) answer is 0.156m

c) so i have done it for 8 strings and is still not correct.

i get $$\frac{4}{321}$$

 

[Redbelly98]

Please show your work.

 

[Paymemoney]

$$\frac{1}{642} * 8$$

 

[Redbelly98]

Sorry about not replying sooner, somehow I missed that you had responded. Not sure if you still want to work this out, but here goes...

$$\frac{1}{642} * 8$$

Not quite. Let's look at the equation you wrote earlier:

c) i tried to use the $$\frac{1}{k_t} = \frac{1}{k_1} + \frac{1}{k_2}$$

k_t is the 642 N/m you found for part (a).

The right-hand-side of this equation would be, for 8 springs,

(1/k₁) + (1/k₂) + ... + (1/k₈)​

 

[Paymemoney]

so to start off would it be something like this:
$$642 =(1/k_1)+(1/k_2)+(1/k_3)+(1/k_4)+(1/k_5)+(1/k_6)+(1/k_7)+(1/k_8)$$

 

[Redbelly98]

so to start off would it be something like this:
$$642 =(1/k_1)+(1/k_2)+(1/k_3)+(1/k_4)+(1/k_5)+(1/k_6)+(1/k_7)+(1/k_8)$$

Not quite. The left-hand side should be 1/k_t, not simply k_t.

Another hint: as it says in the problem statement, the 8 individual springs are identical.

 

[Paymemoney]

so it would be like this:

$$\frac{1}{642} = \frac{1}{k_n}$$

 

[louza8]

If the springs are identical and you've calculated that in series they have a spring constant of k = 642, shouldn't each individual spring have a spring constant of 642? What am I missing in this problem?

 

[Paymemoney]

no, because the 642 is the spring constant for the long spring which is constructed of 8 short springs.

And the thing i am trying to find is the spring constant for each short spring.

 

[louza8]

But the short springs are identical. When they're linked in series, the spring constant won't change.

Eg. if I have two identical springs with k=16N/m^2 for each then when they are in series the 'new spring' has a spring constant of 16N/m^2. However, if they are in parallel the spring constant would be considered to be 32N/m^2.

Applying this to your problem considering the springs are in series and identical, then each individual spring should have 642N/m^2??

 

[Paymemoney]

well that's not what my answer says.

It is 5139.2N/m

 

[louza8]

that would be the answer if they were in parallel, but they're in series.

 

[Redbelly98]

But the short springs are identical. When they're linked in series, the spring constant won't change.

This is simply not true. The spring constant does indeed change for springs in series. For the same amount of applied force, each spring stretches by a smaller amount than the entire assembly. So the spring constant must be different.

so it would be like this:

$$\frac{1}{642} = \frac{1}{k_n}$$

Uh, no, it would be

1/642 = 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n​

Use basic algebra to solve that equation for k_n.

Since I have probably given enough hints now, and you have the final answer to check your work, I'll leave you on your own to finish this one off. Good luck!

 

[louza8]

sorry for the misinformation!

 

[Paymemoney]

This is simply not true. The spring constant does indeed change for springs in series. For the same amount of applied force, each spring stretches by a smaller amount than the entire assembly. So the spring constant must be different.


Uh, no, it would be

1/642 = 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n + 1/k_n​

Use basic algebra to solve that equation for k_n.

Since I have probably given enough hints now, and you have the final answer to check your work, I'll leave you on your own to finish this one off. Good luck!

yep i got the answr, thanks for the help