Calculating the Spring Constant k of a Spring

[jimithing71]

To stretch a spring a distance of 0.20m 30J of work is done. What is the value of the spring constant k of the spring?
a)6 b)30 c)150 d)1500 e)none of the above



I know that the answer is D 1500 but I can't quite arrive at that.



The two formulas I thought to try were F=-kx and PE=1/2kx^2 but those didn't work. Then, after a bit of perusing on here I found k=mg/x.
Thus, 30(9.8)/.20 = 1470 ...which is close to 1500 but is that correct??

 

[Doc Al]

The two formulas I thought to try were F=-kx and PE=1/2kx^2 but those didn't work.

Try again. Note that these formulas are for very different things. Only one of them relates to work/energy.

Then, after a bit of perusing on here I found k=mg/x.

Nah.

 

[jimithing71]

My head is starting to hurt! LOL!

Okay, so now I tried F=-kx, 30J=-k(.20m), 30J/.20m=-k, 150=k

That is one of the options (C), but our instructor told us the answer was (D) 1500. ?

 

[Doc Al]

My head is starting to hurt! LOL!

Okay, so now I tried F=-kx, 30J=-k(.20m), 30J/.20m=-k, 150=k

That is one of the options (C), but our instructor told us the answer was (D) 1500. ?

You picked the wrong equation. F is force, not work. (PE is energy/work)

One more time.

 

[jimithing71]

Thank you! PE=1/2kx^6, 30=1/2k(.04), 30/.04=1/2k(.04)/.04, 750=1/2k, 1500=k Whew!

One more?

A roller coaster car with a mass of 900kg starts at rest from a point 20m above ground. At point B it is 12m above ground. If the initial KE was 0 and the work done against friction between the starting point and point B is 30,000J, what is the KE at point B?
a)10.8kJ b)20kJ c)30dj d)40kJ e) none of the above.

I know the answer is 40 kJ but I'm not sure which equation to use at all. The only one in my notes that seems close is KE=1/2mv^2 but that isn't working.

 

[Doc Al]

The only one in my notes that seems close is KE=1/2mv^2 but that isn't working.

You need to worry about total mechanical energy: KE + PE. What's the formula for gravitational PE?

 

[jimithing71]

G=6.67X10^-11* N*m^2/kg^2 ??

 

[jimithing71]

Or wait! Is it PE=mgh??

 

[cupid.callin]

yes it is

 

[jimithing71]

yes it is

Which one?

 

[Doc Al]

Or wait! Is it PE=mgh??

That's the one.

 

[jimithing71]

Sorry but I don't get that at ALL! That would be PE=(900kg)(9.8g)(20m), PE= 176,400? What am I missing?

 

[Doc Al]

Sorry but I don't get that at ALL! That would be PE=(900kg)(9.8g)(20m), PE= 176,400? What am I missing?

You need to compare total mechanical energy at the starting point to that at point B. What happens to the total mechanical energy because of friction?

 

[jimithing71]

It would be slowed due to friction? I am really lost on this one. I did the PE=mgh for point A and for point B and subtracted the two and got 70,560 so obviously that is wrong as well.

 

[Doc Al]

It would be slowed due to friction? I am really lost on this one. I did the PE=mgh for point A and for point B and subtracted the two and got 70,560 so obviously that is wrong as well.

Hint: If there were no friction, then:

KE_A + PE_A = KE_B + PE_B

How would you have to modify this to incorporate the energy lost to friction?

 

[jimithing71]

I wish I knew!

Okay, last attempt:
KE(a) + PE(a) = KE(b) + PE(b)
0 + 176,400 = KE(b) + 105,840 + 30,000
176,400 - 105,840 - 30,000 = KE(b)
40,560 = KE(b)

?

 

[Doc Al]

I wish I knew!

Okay, last attempt:
KE(a) + PE(a) = KE(b) + PE(b)
0 + 176,400 = KE(b) + 105,840 + 30,000
176,400 - 105,840 - 30,000 = KE(b)
40,560 = KE(b)

?

Looks OK to me. One of the answer choices is pretty close.

 

[jimithing71]

Is that it?

 

[Doc Al]

Is that it?

Yep. (Round off to one significant figure.)

 

[jimithing71]

LOVE YOU Doc Al! Thanks for all your help! Time for a glass of vino! :0)