# Simple harmonic motion problem

1. Jul 30, 2016

### Erenjaeger

1. The problem statement, all variables and given/known data
A 45.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 6.00 cm on a frictionless, horizontal surface.
a) find the total energy of the system (mJ)

2. Relevant equations
1/2KA^2

3. The attempt at a solution
Is the force constant the same as the spring constant 'K' here ? or will i need to determine 'K' by using Hooke's Law? f=-kx and then rearrange for -k=f/x?
also does the A have to be converted into m or can i just plug in 6.00cm?

2. Jul 30, 2016

### TSny

Yes.
There is no way to determine K this way by using information given in the problem.
Try plugging the numbers into the formula along with the units and see what units you end up with for the energy.

3. Jul 30, 2016

### Erenjaeger

n⋅m cm2 ??

4. Jul 30, 2016

### TSny

Not quite. Note that K has units of Newtons per meter.

5. Jul 30, 2016

### Erenjaeger

yeah so n/m but then then amplitude has units of cm with the ^2 there so unless i convert amplitude into m maybe??

6. Jul 30, 2016

### TSny

If you can get the energy in Joules, then it won't be hard to convert to mJ. Can you relate the Joule to the Newton and the meter?

7. Jul 30, 2016

### Erenjaeger

right so the answer i was getting was in joules because joules is n/m or kg⋅m^2⋅s^2 so is mJ millijoules or megajoules ?

8. Jul 30, 2016

### TSny

J ≠ N/m. Did you mean to write N⋅m rather than N/m?
Also, did you mean to write kg⋅m^2/s^2 instead of kg⋅m^2⋅s^2?
mJ stands for milliJoule. MegaJoule would be MJ.

9. Jul 30, 2016

### Erenjaeger

yeah i thought K had a unit of Newtons per meter ?
right so they want the answer i got but in milliJoule?

10. Jul 30, 2016

### TSny

Yes, K has units of N/m. But what about energy? How would you express the Joule in terms of N and m?
Yes, they want the answer in milliJoules.

11. Jul 30, 2016

### TSny

In the formula E = (1/2)KA2 suppose you used N/m for the units of K and cm for the unit of A. What would you get for the units for E? Would you end up with units corresponding to Joules?

12. Jul 30, 2016

### Erenjaeger

would you get N⋅m⋅cm2 ??

13. Jul 30, 2016

### TSny

No. The units for K are N/m, not N⋅m.

14. Jul 30, 2016

### Erenjaeger

dude i am so lost, can you not just explain it to me so i can learn about what youre talking about?

15. Jul 30, 2016

### TSny

If you use K = 40.0 N/m and A = 6.00 cm in the formula E = (1/2)KA2, what do you get for an answer for E (including units)?

16. Jul 30, 2016

### Erenjaeger

120 N/m⋅cm2 since the amplitude is given in cm.??

17. Jul 30, 2016

### TSny

Yes, that's right. Does N/m⋅cm2 represent Joules?

[EDIT: Sorry, I was only looking at the units. You got the units right, but the numerical value is not 120.]

18. Jul 30, 2016

### Erenjaeger

doesnt a joule equal a N⋅m ??

19. Jul 30, 2016

### TSny

Yes, good. So using 6 cm for A does not yield N⋅m (or Joules) for E.

20. Jul 30, 2016

### Erenjaeger

oh yeah so for N⋅m would i just convert amplitude to meters? but then im still left with N/m⋅cm2 does the cm2 part affect anything?