Conservation of Potential Energy?

In summary, when Tarzan swings from the cliff, the force on the vine is equal to the change in kinetic energy.
  • #1
gbdusty
9
0
A block of mass m = 3.6 kg is dropped from height h = 73 cm onto a spring of spring constant k = 1470 N/m . Find the maximum distance the spring is compressed.

I tried calculating the gravitational potential energy (mgy) then setting it equal to 1/2kx^2. but its not working out, can anyone help me out?
 
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  • #2
It should work out. Did you convert the height h into meters?
 
  • #3
Is that because when the spring is compressed the mass falls a little bit further and loses more gpe?

So the change in position of the block is 73cm + x, not just 73cm?
 
Last edited:
  • #4
i converted it into meters, and it doesn't work out still. i don't know what's wrong. actually someone else posted this same question earlier and tried the same method and also got it wrong
 
  • #5
You have the right idea, this should work.

Did you use meters? (not cm)
Did you include the distance x in addition to the height the mass fell?
 
  • #6
no i did not include .73m in addition to x, I am a bit confused by this can someone explain it a little more to me?
 
  • #7
The block falls 73cm and hits the top of the spring.

The spring compresses. Does the block stay at the height where the top of the spring was[/], suspended in free air? No, it falls a little bit further, a distance equivalent to the compression of the spring.

So mgh is mg(0.73 + x)

Equate this to you energy stored in the spring and you get a quadratic to solve for x.
 
  • #8
ok I am trying to solve the quadratic right now, think i made a mistake though i got a really large number
 
  • #9
What is your quadratic? And do you know what the answer should be?
 
  • #10
735x^2 - 35.28x - 25.7544 = 0
not working I am getting a very large incorrect number
 
  • #11
i don't know what the answer should be i have to input answers online, and so far they have been incorrect
 
  • #12
gbdusty said:
735x^2 - 35.28x - 25.7544 = 0
not working I am getting a very large incorrect number
How large? The positive solution to this equation is about 0.22m. The equation is correct.
 
  • #13
yes, i was making very foolish mistakes figured it out eventually. But now I am having problems with this question:

Tarzan, who weighs 629 N, swings from a cliff at the end of a convenient vine that is 21 m long. From the top of the cliff to the bottom of the swing, he descends by 4.9 m. The vine will break if the force on it exceeds 1430 N. What would the greatest force on the vine be during the swing?

I am thinking i should set the initial gravitational potential energy equal to the kinetic energy at the bottom of the swing, calculate for v find centripetal accelaeration and use that to calculate the force on the vine. However, I do not know how I can calculate the value of the initial potential energy if I do not know the height of the cliff. Can someone explain that part to me please?
 

Related to Conservation of Potential Energy?

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, such as kinetic energy.

2. How is potential energy conserved?

Potential energy is conserved when there is no change in the total amount of potential energy within a system. This means that the energy cannot be created or destroyed, but can only be converted from one form to another.

3. What are the different types of potential energy?

There are several types of potential energy, including gravitational potential energy, elastic potential energy, chemical potential energy, and electrical potential energy. Each type is associated with a specific force or field.

4. How does potential energy play a role in everyday life?

Potential energy is present in many everyday activities, such as when a ball is held above the ground, a spring is compressed, or a battery is charged. It is also important in natural phenomena, such as the water cycle and the formation of fossil fuels.

5. What are some real-life applications of the conservation of potential energy?

The conservation of potential energy is essential in many fields, including engineering, physics, and environmental science. It is used to design structures, analyze motion and forces, and understand natural processes such as the flow of water and the formation of geological features.

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