How Do You Calculate Velocity and Height Using Conservation of Energy?

[lostinphysics1]

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

 

[iRaid]

KE_i+PE_i=KE_f+PE_f

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

 

[lostinphysics1]

KE_i+PE_i=KE_f+PE_f

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

 

[iRaid]

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:
\frac{1}{2}mv^2_i+mgh_i=\frac{1}{2}mv^2_f+mgh_f

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

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

 

[lostinphysics1]

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:
\frac{1}{2}mv^2_i+mgh_i=\frac{1}{2}mv^2_f+mgh_f

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

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!

 

[lostinphysics1]

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?

 

[iRaid]

Nope I get the same answers as him, did you even do what I said before?

 

[lostinphysics1]

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

 

[iRaid]

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.

 

[lostinphysics1]

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