Car Oscillates - What's Its Mass?

[Pat2666]

Another question from me yet again!

Two geekie physics students with a combined mass of 124 kg jump into their old car to run out for some late night pizza. The distance between the front and back axles of the car is 2.8 m. When they get in the car, the springs compress a total of 8.7 cm. On their way to the Pizza Hut, when they go over a bump, the car oscillates up and down with a period of 1.5 seconds.
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(a) What is mass of the car?
mcar = kg

HELP: What two quantities determine the period of a mass oscillating on a spring?
HELP: How can you find the combined spring constant for all the springs of the car?

Okay, so based on the HELP provided I believe I thought I knew how to approach the problem. See below :

http://img511.imageshack.us/img511/1138/06162008082256pmix7.jpg

However, do I use 124kg as the mass or should it be 124 + mcar? And if so, then I have two unsolved variables :-\

Even if 124kg is correct I don't understand how solving for the constant k will help me in determining the mass of the car.

Any help would be great! My goal is to understand what I'm doing in the end lol

 

[Pat2666]

T/2*Pi should be 2*Pi/T, I wrote it wrong above.

 

[alphysicist]

Hi Pat2666,

I think it's the total mass of car + passengers.

Try using the fact that the springs compress a total of 8.7 cm after the students got in the car. (They say total because the springs were already compressed some due to the weight of the car.)

 

[Pat2666]

Right, but even if I use that to solve for k, I don't see how that'll help me determine the mass of the vechile :-\

 

[Pat2666]

Okay, well I tried to approach the problem from another direction, but I'm still not getting the correct mass of the car :(

I tried to solve k in a different manner and then use that to solve for Mcar in the equation I was going to use initially. I'm really confused now lol


My Work :

http://img377.imageshack.us/img377/9450/workxm1.jpg

 

[alphysicist]

Hi Pat,


The things they describe as happening (for example, the springs compressing by 8.7 cm) are occurring in response to the total mass of (passengers + car). In the last post, you used:


m g = k x

which is right, but since x = 8.7 cm, m = 124+m_{car}

When you use the period formula, you'll get the same thing, and you'll have two equations in two unknowns.

 

[Pat2666]

Okay, well I set the two equations equal to a common variable to solve for it, but I end up with both constants (k) cancling each other out. And if I solve for k the mass just comes out to 124kg which isn't right :-\

My work :

http://img368.imageshack.us/img368/4701/workxi1.jpg

 

[alphysicist]

I see what you mean. My guess is that when they say the springs compress a total of 8.7 cm, they really mean the springs stretch an additional 8.7 cm.

So let's go back to your post #5:

Okay, well I tried to approach the problem from another direction, but I'm still not getting the correct mass of the car :(

I tried to solve k in a different manner and then use that to solve for Mcar in the equation I was going to use initially. I'm really confused now lol


My Work :

http://img377.imageshack.us/img377/9450/workxm1.jpg

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So your value for k is correct. Now when you use that in the period formula, you need the total mass in the numerator, but you seem to be subtracting them (you have m-124). If you correct that, I think you'll get the right answer. What do you get?

 

[Pat2666]

Oh okay! I have no idea why I subtracted 124kg instead of adding it, but that was the problem. Thanks!

The mass turned out to be 672.88kg for the car :)