How Does Kinetic Energy Affect Spring Compression in Simple Harmonics?

[roughneck84]

[SOLVED] Plz help w/ Simple harmonics question

I am doing simple harmonics and running into problems. The formulas given for simple harmonis in my book are f=[1 / 2(pi)]square_root (k /m) or
f=[1 / 2(pi)]square_root (a /-x). The question reads:

Car 1 has a spring-loaded rear bumper with a force constant of 840000 N/m. A second vehicle, car 2 (with a mass of 1500 kg), travels at a constant speed of 18 km/h, hitting car 1 in the rear bumper.

a) calculate the kinetic energy for car 2.

for this I used
Ek = ½ mv^2
Ek = ½ (1500 kg)(5 m/s)^2
Ek = 1.9 x 10^4 J

b) calculate the distance that car 1's bumper will compress if car 2 comes to a complete stop after striking it ?

from the information given i can calculate the frequency but from there I can't figure the rest

Also I have another harmonics question. Prove that the maximum speed (V{max}) of a mass on a spring is given by 2(pi)fA.

where f = frequency and A =Amplitude? I'm guessing I have to rearrange one of formulas given at the top of the post. Thanks

 

[Hootenanny]

Your answer to question (a) is correct. For question (b) I offer a hint: consider conservation of energy.

 

[roughneck84]

the law of conservation states that energy cannot be created or destroyed. Would i calculate the potential energy of car 1 and add it to the kinetic energy of car 2?

 

[Hootenanny]

the law of conservation states that energy cannot be created or destroyed. Would i calculate the potential energy of car 1 and add it to the kinetic energy of car 2?

Before the collision, car two has some kinetic energy. When car two collides with car one's bumper, it will compress the spring(s). After the collision, car two comes to a complete stop, assuming that car one's speed remains constant this means that all car two's kinetic energy has been converted to ______________.

 

[roughneck84]

Potential energy ?

 

[roughneck84]

so in this question Ek = Ep? from there where do i go to find the distance traveled by the spring?

 

[roughneck84]

Before the collision, car two has some kinetic energy. When car two collides with car one's bumper, it will compress the spring(s). After the collision, car two comes to a complete stop, assuming that car one's speed remains constant this means that all car two's kinetic energy has been converted to ______________.

Potential energy ? so would Ek=Ep ? from there how do i find the distance that the spring travelled?

 

[Hootenanny]

Potential energy ?

Correct

so in this question Ek = Ep? from there where do i go to find the distance traveled by the spring?

Correct again

from there how do i find the distance that the spring travelled?

What is the expression for the energy stored in a compressed spring?

 

[roughneck84]

Et = 1/2mv^2 + 1/2kx^2
I think i get it. I use the value above that I calculated for Ek, put that as Et in the formula then isolate to solve for x.

 

[Hootenanny]

Et = 1/2mv^2 + 1/2kx^2
I think i get it. I use the value above that I calculated for Ek, put that as Et in the formula then isolate to solve for x.

Correct

 

[roughneck84]

originally i thought that was what i do. however i run into a problem when i do that. If Et = Ek and Ek= 1/2mv^2. If i look at the formula i should get
1900 J = 1900 J + 1/2kx^2.
1900 J - 1900 J = 1/2kx^2
0 = 1/2 kx2
i can't have a 0 divided by 1/2k

 

[Hootenanny]

Note that initially v = 18 km/h therefore, your total energy will be equal to the kinetic energy of car 2 (1900J). After the collision v = 0 (the car has stopped), therefore the kinetic energy term disappears and you're equation becomes,

1900 J = 1/2kx^2

Do you follow?

 

[roughneck84]

well explained I understand thank you very much

 

[Hootenanny]

well explained I understand thank you very much

A pleasure