Calculating Maximum Compression Height of Spring: A Scientific Approach

In summary, the height of the compressed spring at the point of maximum compression can be calculated using the equation x = sqrt[2(mghi-mghf)/k], where x is the height of the compressed spring, m is the mass of the block, g is the acceleration due to gravity, h is the initial height of the block, and k is the spring constant. Plugging in the given values, the height of the compressed spring is 10.25 cm.
  • #1
amlev05
1
0
A 20-cm-tall spring with spring constant 5000 N/m is placed vertically on the ground. A 10.0 kg
block is held 17.0 cm above the spring. The block is dropped, hits the spring, and compresses
it. What is the height of the spring at the point of maximum compression?

Here is what i did, i am just unsure if what i did is correct.

PE=potential energy
PE of the block initially(PEbi) = PE of the spring final(PEsf) + PE of the block final(PEbf)
PEbi = PEsf + PEbf
mghi = .5kx^2 + mghf
x = sqrt[2(mghi-mghf)/k)
in this case hf is equal to x
plugging in the numbers i got x to equal 10.25cm
where x is the height of the compressed srping
 
Last edited:
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  • #2
As per the forum rules, you need to show us your attempt.
For a start, try to form an equation using energy conservation.
 

FAQ: Calculating Maximum Compression Height of Spring: A Scientific Approach

1. What happens to the spring when mass is dropped onto it?

When mass is dropped onto a spring, the spring will compress due to the force of the mass pushing down on it. The amount of compression will depend on the mass and the stiffness of the spring.

2. How does the height of the drop affect the spring?

The height of the drop will affect the amount of potential energy that the mass has when it hits the spring. This potential energy will then be transferred into the spring, causing it to compress more or less depending on the height of the drop.

3. Is there a limit to how much the spring can compress?

Yes, there is a limit to how much a spring can compress. This limit is known as the spring's elastic limit, and once it is reached, the spring will no longer return to its original shape and may even break.

4. How does the stiffness of the spring affect the motion of the mass?

The stiffness of the spring will affect the amount of force required to compress it. A stiffer spring will require more force to compress, resulting in a shorter compression distance and a faster return to its original shape. This will cause the mass to bounce higher and faster.

5. What happens to the energy of the mass when it is dropped onto the spring?

When the mass is dropped onto the spring, its potential energy is converted into kinetic energy as it falls. Once it hits the spring, this kinetic energy is then transferred into the spring, causing it to compress. When the spring returns to its original shape, this energy is converted back into kinetic energy and the mass will continue to move until all the energy is dissipated through friction and other forces.

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