General Rule for Spring Compression?

In summary, we are looking at a block sliding on a frictionless table and compressing a spring with an unknown force constant. To find the amount the spring is compressed, we can use the equation for conservation of energy, which involves the gravitational potential energy and kinetic energy of the block, as well as the potential energy of the compressed spring. From there, we can also use the equations for spring energy and kinetic energy to further solve for the spring compression.
  • #1
FrenchAtticus
10
0

Homework Statement



A block of mass m slides on a horizontal frictionless table with an initial speed. It then compresses a spring of force constant k and is brought to rest. How much is the spring compressed x from it's natural length.




Homework Equations



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  • #2
Conservation of energy.
Whats the energy of a moving block
Whats the energy of a compressed spring
 
  • #3
Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2

energy of a moving block is 1/2mv^2

energy of a compressed spring is potential?

How do I apply these to find how much the spring will compress.
 
  • #4
FrenchAtticus said:
Conservation of energy is mgh1 + 1/2mv1^2 = mgh2 + 1/2mv2^2
No this is only for a falling object mgh2 = gravitational potential energy.

energy of a compressed spring is potential?
Whats the equation for the energy in a compressed spring?
 
  • #5
energy in a compressed spring is F = -Kx

and is conservation of energy m1v1 = m2v2?
 
  • #6
No that's momentum.
Spring energy = 1/2 k x^2
Kinetic energy = 1/2 m v ^2

For conservation of energy you have the ke of the block at the start and the spring energy at the end. So the ke just equals the spring energy.
 

1. What is the general rule for spring compression?

The general rule for spring compression states that the amount of force required to compress a spring is directly proportional to the distance the spring is compressed.

2. How do you calculate the force required to compress a spring?

The force required to compress a spring can be calculated using the formula F = kx, where F is the force in Newtons, k is the spring constant in Newtons per meter, and x is the distance the spring is compressed in meters.

3. How does the spring constant affect the force required for compression?

The spring constant is a measure of the stiffness of a spring. A higher spring constant means the spring is stiffer and will require more force to compress, while a lower spring constant means the spring is more flexible and will require less force to compress.

4. Can the general rule for spring compression be applied to all types of springs?

Yes, the general rule for spring compression can be applied to all types of springs, including coil springs, leaf springs, and gas springs. However, the spring constant may differ depending on the type of spring.

5. What are some practical applications of the general rule for spring compression?

The general rule for spring compression is used in many industries, such as automotive, aerospace, and manufacturing. It is also used in everyday objects, such as mattresses, trampolines, and shock absorbers. It is an important concept in designing and engineering various mechanical systems.

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