How Do You Find the Total Energy in Simple Harmonic Motion?

[Erenjaeger]

Homework Statement

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)[/B]

Homework Equations

1/2KA^2
[/B]

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?[/B]

 

[TSny]

Is the force constant the same as the spring constant 'K' here ?

Yes.

or will i need to determine 'K' by using Hooke's Law? f=-kx and then rearrange for -k=f/x?

There is no way to determine K this way by using information given in the problem.

also does the A have to be converted into m or can i just plug in 6.00cm?

Try plugging the numbers into the formula along with the units and see what units you end up with for the energy.

 

[Erenjaeger]

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.

n⋅m cm² ??

 

[TSny]

n⋅m cm² ??

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

 

[Erenjaeger]

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

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

 

[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?

 

[Erenjaeger]

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?

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 ?

 

[TSny]

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

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?

so is mJ millijoules or megajoules ?

mJ stands for milliJoule. MegaJoule would be MJ.

 

[Erenjaeger]

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.

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

 

[TSny]

yeah i thought K had a unit of Newtons per meter ?

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

right so they want the answer i got but in milliJoule?

Yes, they want the answer in milliJoules.

 

[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?

 

[Erenjaeger]

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?

would you get N⋅m⋅cm² ??

 

[TSny]

would you get N⋅m⋅cm² ??

No. The units for K are N/m, not N⋅m.

 

[Erenjaeger]

No. The units for K are N/m, not N⋅m.

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

 

[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)?

 

[Erenjaeger]

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)?

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

 

[TSny]

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

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.]

 

[Erenjaeger]

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

doesnt a joule equal a N⋅m ??

 

[TSny]

doesnt a joule equal a N⋅m ??

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

 

[Erenjaeger]

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

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

 

[TSny]

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

If you convert the amplitude to meters, then you will not have any cm in your answer.

 

[Erenjaeger]

If you convert the amplitude to meters, then you will not have any cm in your answer.

oh true, so by converting the amplitude to m, I am left with N.m which is the units for joules right?

 

[TSny]

oh true, so by converting the amplitude to m, I am left with N.m which is the units for joules right?

Yes, that's right.