Calculating the Frequency of Vertical Vibration in a Bouncing Car

[Chrisemo]

Hi, I hope somebody can help me.I'm stuck in this problem..I want to make sure I made it right before sending to the teacher.Thank you very much

1. Homework Statement

An 80.0 kg student sits down in his 920 kg car, and his weight causes the causes the car's springs to sink an additional 4.0 x 10-3 m. The student then gets out of his car and bounces it up and down. Treating the system as a simple spring and mass, calculate the frequency for the vertical vibration.

Please give a full detailed explanation of solution

Homework Equations

PEs=1/2Kx^2

f=1/T=1/2pi Square root(m/k)

The Attempt at a Solution

Used conservation of energy using only the boy's mass and found a spring constant k=3. 92x10^5.
With the spring constant added in the 2nd formula with only the mass of the car, found the frequency of 3.3Hz

 

[ehild]

Welcome to PF!

1. Homework Statement

An 80.0 kg student sits down in his 920 kg car, and his weight causes the causes the car's springs to sink an additional 4.0 x 10-3 m. The student then gets out of his car and bounces it up and down. Treating the system as a simple spring and mass, calculate the frequency for the vertical vibration.

Please give a full detailed explanation of solution

Homework Equations

PEs=1/2Kx^2

f=1/T=1/2pi Square root(m/k)

The Attempt at a Solution

Used conservation of energy using only the boy's mass and found a spring constant k=3. 92x10^5.

A car is designed so as it vibrations attenuate very fast.
When the boy sit in his car, the springs lower by an additional 4.0 x 10-3 m in the new equilibrium position. You can not apply conservation energy when calculating the spring constant.
When the boy makes his car move up and down he can do that with appreciable amplitude at the resonant frequency of the car. For that frequency, the formula you quoted is valid.

 

[Chrisemo]

So, what can I use to calculate the spring constant,can I use the sum of the forces normal and mg of the boy? -N+mg=-Kx

 

[SammyS]

So, what can I use to calculate the spring constant,can I use the sum of the forces normal and mg of the boy? -N+mg=-Kx

Use Hooke's Law.

 

[Chrisemo]

Ok, so F= - Kx = mg, but which mass do I use? Car+boy or only boy?

 

[SammyS]

Ok, so F= - Kx = mg, but which mass do I use? Car+boy or only boy?

Hooke's Law is linear. The extra weight causes an extra amount of compression.

 

[Chrisemo]

If the only weight added is the boy's I think it will be
Kx=mg
so,K=(80x9.82)/4.0x10^-3=1.96x10^5

 

[ehild]

If the only weight added is the boy's I think it will be
Kx=mg
so,K=(80x9.82)/4.0x10^-3=1.96x10^5

Yes, it is correct (if you mean N/m)

 

[Chrisemo]

Thank you very much :)