What Is the Total Load Supported by the Springs and the Mass of the Car?

[awertag]

Homework Statement

Two people with a combined mass of 120 kg climb into an old car with worn out shock absorbers causing the springs to compress by 7.36 cm. Then, when the car hits a bump in the road it oscillates up and down with a period of 1.35 s.

(1) Find the total load supported by the springs.

(2) Find the mass of the car.

Homework Equations

T = 2pi (m)**.5 / (k)**.5

pi as in 3.1415... T= period k=spring constant **.5 as in radical

also note /\ means: delta/change in

The Attempt at a Solution

Fsp=mg
k/\x=mg
k(.0736)=(120)(9.8)
k=15978.2609 N/m


then plug into above equation:

1.35=[2pi(m)**.5]/(15978.2609)**.5

got incorrect answer of m= 71851.6587 kg

good help would be greatly appreciated!

 

[Rick88]

use k$$\Delta$$x = mg to find k. To do this, use the information given when the car is at rest. So m=120kg, $$\Delta$$x = 7.36cm .

Once you found k, plug the value in the other equation ( T = 2$$\pi$$ ...) to find m.R.

 

[awertag]

thanks for replying rick, but that's what i did...i believe. Can you show me the difference?

 

[Rick88]

You are absolutely, right. I beg your pardon.

However, my answer for m is completely different from yours.
I get m = 738kg.

Try solving again the second equation.
I would suggest you to square both sides so to get rid of the square root, if you hadn't done so already.

R.

 

[awertag]

Wow, thank you so much! I squared both sides and that did the trick, really cleaned up the algebra. Have a great day! :)

 

[Rick88]

Glad to be of help :)

Thanks, have a great day yourself!R.