How far has the spring been compressed?

In summary, a 9.0 kg block slides down a frictionless incline at 29° and is stopped by a spring with a spring constant of 3.50 x 10^4. The block slides 5.00 m before coming to rest against the spring. Using the equation 1/2kx^2=fxs, the spring is compressed by 5.11 m. This may not yield the correct answer and further calculations are needed to determine the correct compression.
  • #1
A block of mass 9.0 kg slides from rest down a frictionless incline and is stopped by a strong spring with spring constant 3.50 x 10^4 The block slides 5.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

My attempt:

Since during the 5m of motion, energy loss is going to be equal to energy gain,
i should be able to apply this equation
x= length of movement that the spring isn't compressed during.
this doesn't yield the correct answer as x=5.11
what am i doing wrong?
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  • #2
This looks just like:
that you posted yesterday without a spring constant?

Since you are using sin29, I'm guessing that the incline is 29°.

So to solve either of these problems, you know the total energy in the system, from gravitational potential energy.

When it stops then you know how much energy must be in the spring.

From that you can readily figure the compression of the spring.
  • #3

There could be a few things that could be causing the discrepancy in your calculation. First, make sure that your calculation for the force of gravity (9(9.8)sin29) is correct. Also, double check your equation for energy conservation - it should be 1/2kx^2 = mgh, where m is the mass of the block, g is the acceleration due to gravity, and h is the height of the incline. Additionally, make sure that you are using the correct units - the spring constant should be in N/m, and the distance should be in meters. Finally, check your algebra to make sure that you are solving for x correctly. If you are still getting the incorrect answer, try using a different method, such as using the equation for work (W = Fd) to calculate the distance the spring has been compressed.

Question 1: What is the definition of spring compression?

Spring compression is the decrease in length of a spring when a force is applied to it, causing it to store potential energy.

Question 2: How is the amount of spring compression measured?

The amount of spring compression is measured by the change in length of the spring from its original, uncompressed state. This can be measured using a ruler or other measuring tool.

Question 3: What factors affect the amount of spring compression?

The amount of spring compression is affected by the force applied to the spring, the stiffness of the spring, and the original length of the spring.

Question 4: What is the formula for calculating the amount of spring compression?

The formula for calculating spring compression is F = kx, where F is the applied force, k is the spring constant, and x is the amount of compression.

Question 5: How does spring compression relate to potential energy?

Spring compression is directly related to potential energy, as the potential energy stored in a compressed spring is equal to the force applied multiplied by the distance the spring is compressed. This potential energy can be released when the spring is allowed to return to its original length.

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