What is the spring constant of each spring

In summary, a compact car with a mass of 1200 kg and four identical springs bounces up and down at a frequency of 2.0 times per second. The spring constant for each spring is 47326.08 N/m. When carrying four 70 kg passengers, the car's oscillation frequency decreases to 0.9 hz due to the increased mass of 1480 kg.
  • #1
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Homework Statement



A compact car has a mass of 1200 kg. Assume that the car has one spring on each wheel, that the spring are identical, and that the mass is equally distributed over the four springs. draw a picture of the situation.
a) what is the spring constant of each spring if the empty car bounces up and down 2.0 times per second?
b) what will be the cars oscillation frequency while carrying four 70 kg passengers.

Homework Equations



f = 1/2pie(k/m)^sq root

The Attempt at a Solution



m = 1200 kg
f = 2 hz

a) k = (2*pie*f)^2 * m = (2*3.14*2hz)^2*1200 kg = 189304.32 N/m

b) m = (4*70)+1200 kg = 1480 kg

f = (1/2*pie)(189304.32 Nm^-1/1480 kg) = 1.8 hz

im not sure where I messed up.
 
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  • #2
rayhan619 said:
a) k = (2*pie*f)^2 * m = (2*3.14*2hz)^2*1200 kg = 189304.32 N/m
There are four springs, not one giant spring.
 
  • #3
so divide k by 4?
 
  • #4
Yes.
 
  • #5
so
a) k = (189304.32 N/m)/4 = 47326.08 N/m

and
b) f = (1/2*pie)(47326.08 Nm^-1/1480 kg)^sq. root = 0.9 hz

is it right?
 
  • #6
rayhan619 said:
so
a) k = (189304.32 N/m)/4 = 47326.08 N/m
OK.

and
b) f = (1/2*pie)(47326.08 Nm^-1/1480 kg)^sq. root = 0.9 hz
No. What's the mass per spring?
 

1. What is the definition of spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

2. How is spring constant calculated?

Spring constant is calculated by dividing the force applied to a spring by the resulting displacement. This is represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

3. What are the units of spring constant?

The units of spring constant depend on the unit of force and displacement used in the calculation. In the SI system, the standard unit for spring constant is newtons per meter (N/m).

4. How does the spring constant affect the behavior of a spring?

The spring constant determines how much a spring will stretch or compress in response to an applied force. A higher spring constant means the spring is stiffer and will require more force to stretch or compress, while a lower spring constant means the spring is more flexible and will require less force.

5. Can the spring constant change?

Yes, the spring constant can change depending on various factors such as the material of the spring, its dimensions, and the temperature. For example, as a metal spring is heated, its atoms vibrate more, causing the spring to become less stiff and the spring constant to decrease.

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