Calculating Vibration Frequency of 1100 kg Car with 68 kg Driver

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In summary, the conversation discusses the calculation of the frequency of vibrations for a car going over a bump. It involves finding the spring constant and the period of oscillation, using the weight of the driver and the compression distance of the springs. The correct method includes converting the units to SI and using the combined mass of the car and driver. The approximate answer for the period is 0.6 seconds.
  • #1
LostTexan07
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The springs of a 1100 kg car compress 6.0 mm when its 68 kg driver gets into the driver's seat. If the car goes over a bump, what will be the frequency of vibrations?

I tried to use the weight of the man (68 kg) and the compression distance (6 mm) to find the spring constant. I then tried to use the spring constant to find the period.

F = kx
68 = 6k
k = 11.33

T = 2(pi)(sq.rt 1100/11.33)

But I didn't get the correct answer.
 
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  • #2
When you calculate k, first convert mm to m. 6.0mm = 6.0*10^-3m

When you calculate T, use the mass of the man = 68kg. not the mass of the car.
 
  • #3
Also, the driver's mass is 68 kg., but you need the added weight of the driver applied to the springs. The spring constant, k, needs to be expressed in SI units, which are Newtons/m, which is why learningphysics corrected your 6 mm entry.

For the period of oscillation, you will need the combined mass of car and driver. (I'll say that the answer is in the neighborhood of 0.6 second.)
 
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  • #4
Yes, sorry you need to use:

F = kx

mg = kx (with m = 68kg) to find k...

I didn't notice the g was missing.

dynamicsolo, I'm not getting 0.6 for the period like that... are you sure about using the combined mass of the car and the person?
 
  • #5
learningphysics said:
dynamicsolo, I'm not getting 0.6 for the period like that... are you sure about using the combined mass of the car and the person?

You do use the total mass (1168 kg.) now resting on the springs for this "oscillator". The figure I gave for the period is approximate because I didn't want to just provide the answer. [k should be around 111,000 N/m and sqrt(m/k) is roughly 0.1 sec.]
 
  • #6
dynamicsolo said:
You do use the total mass (1168 kg.) now resting on the springs for this "oscillator". The figure I gave for the period is approximate because I didn't want to just provide the answer. [k should be around 111,000 N/m and sqrt(m/k) is roughly 0.1 sec.]

Oh, I see my problem. I was thinking the springs described were "in" the driver's seat... sorry about that.

yes, I get around 0.6. I must have been plugging in something wrong.
 

FAQ: Calculating Vibration Frequency of 1100 kg Car with 68 kg Driver

How do you calculate the vibration frequency of a car with a driver?

To calculate the vibration frequency of a car with a driver, you will need to know the mass of the car and the driver. You will also need to know the spring constant of the car's suspension system. Then, you can use the formula f = 1/2π√(k/m) where f is the vibration frequency, k is the spring constant, and m is the total mass of the car and driver.

Why is it important to calculate the vibration frequency of a car with a driver?

Calculating the vibration frequency of a car with a driver is important because it can help identify any potential issues with the car's suspension system. If the vibration frequency is too high, it could indicate that the suspension system is not working properly, which could lead to discomfort for the driver and potential safety hazards.

What is the unit of measurement for vibration frequency?

The unit of measurement for vibration frequency is Hertz (Hz). This measures the number of vibrations or oscillations that occur in one second.

How does the mass of the car and driver affect the vibration frequency?

The mass of the car and driver directly affects the vibration frequency. As the mass increases, the vibration frequency decreases. This means that a heavier car with a heavier driver will have a lower vibration frequency compared to a lighter car with a lighter driver.

Can the vibration frequency of a car with a driver be changed?

Yes, the vibration frequency of a car with a driver can be changed by adjusting the spring constant of the suspension system. A higher spring constant will result in a higher vibration frequency, while a lower spring constant will result in a lower vibration frequency.

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