Conservation of energy - spring

[lukatwo]

Homework Statement

Hello, I'm having a problem with this. So we drop the weight on this spring, and the question is: how much does the spring compress? The mass is 5kg, the height 0,4m, and the spring elasticity factor k=1700N/m.

Homework Equations

The Attempt at a Solution

I've tried to equalize the potential energies of when we drop the weight, and when it's all the way down. It looks like this: m(h+ΔL)=(1/2)*k*(ΔL)^2. I get a quadratic equation, and solve it. I get two answers one with +, and one -. I've tried to enter the positive one, and it's not correct. Should I enter the negative one, or is my whole attempt faulty?

 

[PhanthomJay]

Homework Statement

Hello, I'm having a problem with this. So we drop the weight on this spring, and the question is: how much does the spring compress? The mass is 5kg, the height 0,4m, and the spring elasticity factor k=1700N/m.

Homework Equations

The Attempt at a Solution

I've tried to equalize the potential energies of when we drop the weight, and when it's all the way down. It looks like this: m(h+ΔL)=(1/2)*k*(ΔL)^2. I get a quadratic equation, and solve it. I get two answers one with +, and one -. I've tried to enter the positive one, and it's not correct. Should I enter the negative one, or is my whole attempt faulty?

Looks like you left out g in your gravitational PE term, otherwise, looks good. Think positive.

 

[lukatwo]

Should it be g*m*(h+∆L)=(1/2)*k*(∆L)^2, because if it's on both sides it's the same

 

[PhanthomJay]

Should it be g*m*(h+∆L)=(1/2)*k*(∆L)^2, because if it's on both sides it's the same

Sure!

 

[HalfLostAndSearching]

I would like to clarify that conservation of energy is a fundamental principle in physics which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the scenario described, the energy of the weight is converted into potential energy as it is lifted to a height of 0.4m, and then into elastic potential energy as it compresses the spring.

To solve for the amount of compression of the spring, we can use the equation for elastic potential energy: Ee = (1/2)*k*(ΔL)^2, where Ee is the elastic potential energy, k is the spring constant, and ΔL is the change in length of the spring.

Substituting the given values, we get: Ee = (1/2)*1700*(ΔL)^2 = (1/2)*5*9.8*0.4 = 9.8J

Solving for ΔL, we get ΔL = √(9.8/850) = 0.041m.

Therefore, the spring will compress by 0.041m.

Your attempt at using the potential energy equation is correct, but it seems that you may have made a mistake in your calculations or in setting up the equation. I would suggest double-checking your work and trying again. It is possible that the negative answer you obtained is the correct one, but it is always important to check your work and make sure it aligns with the principles of conservation of energy.