Test Question (Potential Energy): Need help finding answer

In summary, The conversation discusses finding the maximum compression of a spring when a 4kg block is dropped from a height of 0.8m above it. The conversation includes equations and calculations to determine the compression, but there is a discrepancy in the final answer due to not taking into account the gravitational potential energy. The correct equation should be: mg(x_0 + x_{spring}) = 0.5kx_{spring}^2.
  • #1
gokugreene
47
0
I can't figure out what I did wrong on this test question.

A 4kg block is dropped from a height of 0.8m above a spring, k=120N/m. Find the maximum compression of the spring.

I have the PE at the top is equal to KE at the bottom.
PEtop=31.4J
KEbottom=31.4J

The potential energy in the spring when compressed should equal the KE at the bottom. Based upon that I should be able to find the maximum distance the spring will compress.

KEbottom=Wspring
31.4J=.5*120*x^2
Rearranging x=sqrt(2*31.4/120) and I get x=-0.723m

What am I doing wrong here? Can someone point it out.

Thanks, peace
 
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  • #2
Remember that the spring is compressing in the vertical direction, so there is more gravitational potential energy to take into account:

Initial gravitational potential energy = Final spring potential energy

[tex]mg(x_0+x_{spring})=\frac{1}{2}kx_{spring}^2[/tex]
 
Last edited:
  • #3
Your equation will give me the exact same answer I got.
mg(0.8 + 0) =.5kx^2
 
  • #4
gokugreene said:
Your equation will give me the exact same answer I got.
mg(0.8 + 0) =.5kx^2

No, in my response, x_spring is the same as x in your response. On the left side, you set the second term to 0, when it should be mgx. It's a quadratic equation.
 

1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or state. It is stored energy that has the potential to be converted into other forms of energy, such as kinetic energy.

2. How is potential energy calculated?

Potential energy is calculated by multiplying the object's mass by the acceleration due to gravity (9.8 m/s^2) and its height above the ground. The formula for potential energy is PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.

3. What are the different types of potential energy?

The different types of potential energy include gravitational potential energy, elastic potential energy, chemical potential energy, and electric potential energy.

4. Can potential energy be negative?

Yes, potential energy can be negative. This typically occurs when the object has a negative velocity or is in a state of compression, such as a compressed spring or a stretched rubber band.

5. How does potential energy relate to work?

Potential energy and work are closely related. Work is the transfer of energy from one form to another, and the change in potential energy is equal to the work done on an object. This means that when work is done on an object, its potential energy changes by the same amount.

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