Calculate spring constant for cart attached to a spring

In summary, a cart with a mass of 2kg is connected by a spring to a fixed object and executes simple harmonic motion with a period of 4 seconds. The maximum displacement of the cart from its rest position is 1.8m. To calculate the spring constant, the equation F=-kx is used, where F is the force, k is the spring constant, and x is the displacement. The units for the spring constant are N/m. To relate the spring constant, period, and mass, the equation k= 4π²m/T² can be used, where k is the spring constant, m is the mass, and T is the period.
  • #1
SharpCode
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Homework Statement


A Cart is floating on an airtrack and is connected by a spring to one fixed object. The cart executes a simple harmonic motion with a period of 4 seconds. Its mass is 2kg. Its maximum displacement from rest position is 1.8m. Calculate the spring constant and provide units.


Homework Equations


F= -kx


The Attempt at a Solution


The units would be N/m i am guessing but i am still a little lost. k is the spring constant rearranged it should be:
k = F/x right?

COULD A MOD PLEASE REMOVE THIS OR MY OTHER THREAD. INTERNET CUT OUT BUT MUST HAVE SUBMITTED TWICE
 
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  • #2
how do you relate k , period and mass?
 
  • #3
Hey pcm i posted in my other thread

hoping this one gets removed... double posted by accident
 

1. How do you calculate the spring constant for a cart attached to a spring?

The spring constant, also known as the spring stiffness, can be calculated by dividing the force applied to the spring by the displacement of the spring. This can be represented by the equation k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

2. What is the unit of measurement for spring constant?

The unit of measurement for spring constant is Newton per meter (N/m) in the metric system, or pound-force per inch (lbf/in) in the imperial system.

3. How does the mass of the cart affect the spring constant?

The mass of the cart does not affect the spring constant. The spring constant is solely dependent on the spring itself and its material properties.

4. Can the spring constant change?

Yes, the spring constant can change if the material of the spring changes or if the spring is stretched or compressed beyond its elastic limit. The spring constant can also vary slightly due to temperature changes.

5. How is the spring constant used in real-life applications?

The spring constant is used in various real-life applications, such as in car suspensions, door hinges, and shock absorbers. It is also used in designing and testing mechanical and electrical systems to ensure they can withstand certain forces without breaking.

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