Conservation of Energy Help

In summary, the conversation focuses on solving two problems involving finding velocity and height using the equations for potential and kinetic energy. The conversation also touches on the concept of energy conservation and provides an equation to use when solving these types of problems. After some trial and error, the conversation's participants were able to come up with the correct solutions for both problems and hope that this example can help others in similar situations.
  • #1
lostinphysics1
6
0

Homework Statement


I have a homework assignment that I am stuck on using the attached table.

Problem 1: I have to find the velocity when given the mass and height.
Problem 2: Then I have to find the height when given the velocity and mass.

Homework Equations


P.E. = m*g*h
K.E. = 1/2*m*v^2

Mass = 1kg
Gravity = 9.8m/s

The Attempt at a Solution


P.E.(1) = 1kg * 9.8m/s * .5m
P.E.(1) = 4.9J

P.E.(2) = 1kg * 9.8m/s * .2m
P.E.(2) = 1.96J

K.E.(1) = 0m/s

K.E.(2) = 1/2*1kg*(.8m)^s
K.E.(2) = .32J

K.E.(1) + P.E.(1) = K.E.(2) + P.E.(2)
0m/s+4.9J = 1/2*1kg*v^2 + 0J
4.9J = .5*v^2
4.9J*.5=v^2
√2.45J=v^2
2.45 m/s = v

I am not sure about how to get the height.

Thank you for any help
 

Attachments

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  • #2
[tex]KE_i+PE_i=KE_f+PE_f[/tex]

Just use that and change out the KE's and PE's with their respective formulas.
 
  • #3
iRaid said:
[tex]KE_i+PE_i=KE_f+PE_f[/tex]

Just use that and change out the KE's and PE's with their respective formulas.

But that will only provide data in Joules and not a velocity or height?

Thank you
 
  • #4
lostinphysics1 said:
But that will only provide data in Joules and not a velocity or height?

Thank you

Think about it, the first law of energy conservation is that the total energy of an isolated system cannot change (or cannot be created nor destroyed), so whenever something happens, something else has to counteract it. If you have an initial KE and PE, you have to have a final KE and PE.

So, the equation becomes:
[tex]\frac{1}{2}mv^2_i+mgh_i=\frac{1}{2}mv^2_f+mgh_f[/tex]

All the mass values cancel and you're left with:
[tex]\frac{1}{2}v^2_i+gh_i=\frac{1}{2}v^2_f+gh_f[/tex]

Now all you do is plug in those values you have in the table.
 
  • #5
iRaid said:
Think about it, the first law of energy conservation is that the total energy of an isolated system cannot change (or cannot be created nor destroyed), so whenever something happens, something else has to counteract it. If you have an initial KE and PE, you have to have a final KE and PE.

So, the equation becomes:
[tex]\frac{1}{2}mv^2_i+mgh_i=\frac{1}{2}mv^2_f+mgh_f[/tex]

All the mass values cancel and you're left with:
[tex]\frac{1}{2}v^2_i+gh_i=\frac{1}{2}v^2_f+gh_f[/tex]

Now all you do is plug in those values you have in the table.

I will have to dust off my algebra book to move the variables around as the information in the chart is provided.
I will try it in the morning see what I get.

Thanks for the help!
 
  • #6
lostinphysics1 said:
I will have to dust off my algebra book to move the variables around as the information in the chart is provided.
I will try it in the morning see what I get.

Thanks for the help!

I emailed the teacher and asked for help but he provided answers:
Problem #1: 2.42 m/s^2
Problem #2: .259 m

When I input the values from the chart I do not get the answers he provided. So, I am not sure what I am doing wrong.

Does anyone else get the same solutions mentioned above?
 
  • #7
Nope I get the same answers as him, did you even do what I said before?
 
  • #8
iRaid said:
Nope I get the same answers as him, did you even do what I said before?

Yes, I tried but I had no way to know if the answers I got are correct so I sent the answers I had. Which as it turns out had been wrong.

But I think I finally got Problem 1.

P.E.i = 4.9J
K.E.i = 0J
P.E.f = 1.96J
K.E.f = ?

K.E.i + P.E.i = K.E.f + P.E.f
0J + 4.9J = 1/2 * 1kg * (v)^2 + 1.96J
4.9J = .5 *(v)^2
-1.96 = .5 * (v)^2
2.94 = .5 * (v)^2
/.5 = (v)^2
5.88 = (v)^2
√5.88 = √(v)^2
2.42 = V

Now to try Problem 2

Thank you
 
  • #9
lostinphysics1 said:
Yes, I tried but I had no way to know if the answers I got are correct so I sent the answers I had. Which as it turns out had been wrong.

But I think I finally got Problem 1.

P.E.i = 4.9J
K.E.i = 0J
P.E.f = 1.96J
K.E.f = ?

K.E.i + P.E.i = K.E.f + P.E.f
0J + 4.9J = 1/2 * 1kg * (v)^2 + 1.96J
4.9J = .5 *(v)^2
-1.96 = .5 * (v)^2
2.94 = .5 * (v)^2
/.5 = (v)^2
5.88 = (v)^2
√5.88 = √(v)^2
2.42 = V

Now to try Problem 2

Thank you

First one is correct, now do the same for the 2nd, but you're trying to find the final height now.
 
  • #10
iRaid said:
First one is correct, now do the same for the 2nd, but you're trying to find the final height now.

Did Problem 2 similar to the first.

P.E.i = m*g*h
P.E.i = 1kg * 9.6m/s * .3m
P.E.i = 2.94J

K.E.i = 1/2 * m * (v)^2
K.E.i = 1/2 * 1kg * (.8m/s)^2
K.E.i = .32J

K.E.f = 1/2 * m * (v)^2
K.E.f = 1/2 * 1kg * (1.2m/s)^2
K.E.f = .72

Need P.E.f

P.E.i + K.E.i = P.E.f + K.E.f
2.94J + .32J = 1kg * 9.8m/s * h + .72J
3.26J = 1kg * 9.8m/s * h + .72J
-.72J - .72J
2.54J = 1kg * 9.8m/s * h
2.54J = 9.8 kg*m/s * h
2.54J/9.8 kg*m/s = h
.259 m = h

Seems my answer matches up with the teachers.

Thank you for the help

Hopefully this example helps others
 

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another.

Why is the conservation of energy important?

The conservation of energy is important because it is a fundamental principle in physics that helps us understand and predict the behavior of physical systems. It also plays a crucial role in sustainable energy practices and environmental conservation.

What are some examples of energy conservation?

Examples of energy conservation include turning off lights and electronics when not in use, using energy-efficient appliances, using public transportation, and choosing renewable energy sources.

How does the conservation of energy apply to everyday life?

The conservation of energy applies to everyday life in various ways, such as in the use of energy-efficient technology, mindful consumption of resources, and active efforts to reduce energy waste. It also helps individuals make informed decisions about their energy use and its impact on the environment.

What are the consequences of not conserving energy?

The consequences of not conserving energy include depletion of natural resources, increased pollution and greenhouse gas emissions, and higher energy costs for individuals and businesses. It also contributes to climate change and other environmental issues.

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