Calculating the max distance of compression of the spring HELP

Therefore, the maximum distance the spring is compressed is 10 cm. In summary, the conversation is about calculating the maximum distance of compression of a spring when a 2.0 kg block is dropped from a height of 40 cm onto the spring with a force constant of 1960 N/m. The attempt at a solution involved using the equations W=mgh and W=1/2kx^2, but the answer was incorrect. The correct answer is 10 cm, taking into account the extra gravitational potential energy from the distance the spring drops through while touching the block.
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Calculating the max distance of compression of the spring please HELP!

Homework Statement


A 2.0 kg block is dropped from a height of 40 cm onto a spring of force constant k = 1960 N/m. The maximum distance the spring is compressed is?


Homework Equations


I Used the equation W=mgh and W=1/2kx^2..


The Attempt at a Solution


i did..
W=2*9.8*0.4
=7.84
then i used
7.84=1/2*1960*x^2
from which i got x=0.0894427191
then i did
7.84*0.0894427191=0.7012309177
then i did
7.84-0.7012309177=7.13879

can anyone please help me tel where i went wrong? because the answer to this question is 10 but i don't know how to get it..please help=].
 
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There is extra gravitational potential energy from the distance through which the spring drops through while touching the spring. In other words, the total distance that the object drops is 40 cm plus however far the spring compresses.
 

FAQ: Calculating the max distance of compression of the spring HELP

1. What is the formula for calculating the max distance of compression of a spring?

The formula for calculating the max distance of compression of a spring is d = (Fmax - F0) / k, where d is the distance, Fmax is the maximum force applied, F0 is the initial force, and k is the spring constant.

2. How do I determine the spring constant for a specific spring?

The spring constant can be determined by dividing the force applied by the change in length of the spring. This can be done by measuring the length of the spring when no force is applied and then measuring the length again when a known force is applied.

3. Can I use the same formula for calculating the max distance of compression for any type of spring?

No, the formula may differ for different types of springs. For example, the formula for a linear spring may be different from that of a torsion spring. It is important to use the correct formula for the specific type of spring being used.

4. What units should be used when plugging in values for the formula?

The units used for the force and distance should be consistent. For example, if the force is measured in Newtons, then the distance should be measured in meters. It is important to use the same units to ensure accurate results.

5. Is there a limit to the max distance of compression for a spring?

Yes, there is a limit to the max distance of compression for a spring. Once the spring reaches its elastic limit, it will no longer return to its original shape and may be permanently deformed. It is important to stay within the elastic limit to avoid damaging the spring.

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