Spring Constant when compressed

In summary, the problem involves a 6kg block sliding down a frictionless ramp and compressing a horizontal spring by 45 cm. By using the equations for gravitational potential energy and elastic potential energy, the spring constant can be determined by setting the two equations equal to each other.
  • #1
cdsnig
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Homework Statement



A 6kg block is released from the top of a 1.0m ramp (frictionless) and slides into a horizontal spring, compressing it 45 cm. Determine the spring constant.



Homework Equations



PEg = mgh (6*9.8*1) = 58.8

PEs = 1/2kx^2 (1/2*k*.45^2)



The Attempt at a Solution



Do I set the two equations equal to each other and get 582.2 as the spring constant?
 
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  • #2
Welcome to PF,

Yeah that seems like the right approach to use: energy conservation. All of the gravitational PE that the object had at the top of the ramp is converted into KE by the time it reaches the bottom of the ramp, and then into elastic PE as it compresses the spring. So assuming no losses due to friction, you can equate the initial and final PE.
 

1. What is the definition of spring constant when compressed?

The spring constant when compressed refers to the measure of how much a spring will compress when a force is applied to it. It is represented by the symbol k and is measured in units of force per unit length (N/m).

2. How is spring constant when compressed calculated?

The spring constant when compressed can be calculated by dividing the applied force by the amount of compression 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 amount of compression.

3. What factors affect the spring constant when compressed?

The spring constant when compressed is affected by the material and shape of the spring, the amount of coils, and the diameter of the wire used to make the spring. Additionally, temperature and external forces can also impact the spring constant.

4. How does the spring constant when compressed relate to Hooke's Law?

Hooke's Law states that the force exerted by a spring is directly proportional to the amount of compression or elongation of the spring. Therefore, the spring constant when compressed is a measure of the proportionality constant in Hooke's Law.

5. How is the spring constant when compressed used in real-world applications?

The spring constant when compressed is used in various real-world applications, such as in the design of suspension systems for vehicles, shock absorbers, and even in sports equipment like trampolines. It is also used in scientific experiments to measure the stiffness of materials and to study the effects of forces on springs.

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