How to Calculate Energy Change for Lifting an Object on Earth and the Moon?

[Lil Uzi Vert]

Homework Statement

A person performs 6.1 J of work to lift an object without acceleration to a particular height on Earth. Write an equation describing that energy change and analyze it to determine how different the energy would be required to lift the same object to the same height on the moon where the value of g is 1.622 m/s^(2).

No height is given.
No mass is given.
No displacement is given.

Homework Equations

W= F*D
Eg=mgh
P=W/T

The Attempt at a Solution

I tried using the power equation but we only have work as energy (6.1 J) and no time or power.
Using W=FD, i was able to make two equations
1. 6.1= m*9.8*h*D
2. E= m*1.622*h*D
After that i did not know where to go from there.
I'm stuck on this question and have no clue how to create this equation describing the energy change to find the energy required to lift the object to the same height on the moon.

Please help!

 

[PeroK]

The Attempt at a Solution

I tried using the power equation but we only have work as energy (6.1 J) and no time or power.
Using W=FD, i was able to make two equations
1. 6.1= m*9.8*h*D
2. E= m*1.622*h*D
After that i did not know where to go from there.
I'm stuck on this question and have no clue how to create this equation describing the energy change to find the energy required to lift the object to the same height on the moon.

Please help!

You've nearly done this problem without realising it. That said, it isn't clear to me exactly what they are looking for. But, perhaps, any correct answer will do.

One mistake, however, is why do you have $h*D$ in your equations?

Also, if you are going to use any numbers like $9.8$ you are going to have to put units on everything. Alternatively, use $g$ or $g_e$ for the Earth's surface gravity and leave the numbers out of the equations.

 

[berkeman]

1. 6.1= m*9.8*h*D
2. E= m*1.622*h*D

The h is the D in these equations, so just use D for the height change.

Oops, beaten by PeroK again!

 

[Lil Uzi Vert]

I am having trouble with these two equations because I do not know how to create them into what the question is looking for. Can I have a hint?

 

[PeroK]

I am having trouble with these two equations because I do not know how to create them into what the question is looking for. Can I have a hint?

Here's what I would do:

1) I would describe the sort of energy we are talking about.

2 Because we have two scenarios (Earth and moon), I would use $E_1$ for the Earth and $E_2$ for the moon.

3) I would do the equation all in letters and then, separately, state what quantities we know.

So, for the first one I would do:

Let $E_1$ be (you have to describe what energy we are talking about here)

Then:

$E_1 =$ (your equation involving $m, g, h$ etc.)

Where $E_1 = 6.1J$

 

[gneill]

Hi Lil Uzi Vert, Welcome to Physics Forums!

A handy way to proceed in these sorts of problems is to form ratios from your formula. Best to start with symbols and plug in numbers later. So let:

$M$ be the mass of the object (same for both cases)
$h$ be the height (same for both cases)
$g_e$ be the gravity on Earth
$g_m$ be the gravity on the Moon (that's your 1.622 m/s^2)
$w_e$ be the work done on Earth (that's your 6.1 J)
$w_m$ be the work done on the Moon

Write the expressions (symbolically) for the work done in each case, then form ratios from the two sides of the equations. Solve for your unknown value.

For example, suppose you had a general expression for some quantity: $f = a*x$ and you had one case where you know all the values: $f_1 = a_1*x_1$, but you have another case where the constant $a$ is different and you don't know what $f_2$ will be. Then you first write out the two cases:

$f_1 = a_1 * x_1$
$f_2 = a_2*x_2$

Form ratios:

$\frac{f_1}{f_2} = \frac{a_1 * x_1}{a_2 * x_2}$

If you can fill in values for all but one of the variables then you can solve for that variable.

 

[Lil Uzi Vert]

Hi Lil Uzi Vert, Welcome to Physics Forums!

A handy way to proceed in these sorts of problems is to form ratios from your formula. Best to start with symbols and plug in numbers later. So let:

$M$ be the mass of the object (same for both cases)
$h$ be the height (same for both cases)
$g_e$ be the gravity on Earth
$g_m$ be the gravity on the Moon (that's your 1.622 m/s^2)
$w_e$ be the work done on Earth (that's your 6.1 J)
$w_m$ be the work done on the Moon

Write the expressions (symbolically) for the work done in each case, then form ratios from the two sides of the equations. Solve for your unknown value.

For example, suppose you had a general expression for some quantity: $f = a*x$ and you had one case where you know all the values: $f_1 = a_1*x_1$, but you have another case where the constant $a$ is different and you don't know what $f_2$ will be. Then you first write out the two cases:

$f_1 = a_1 * x_1$
$f_2 = a_2*x_2$

Form ratios:

$\frac{f_1}{f_2} = \frac{a_1 * x_1}{a_2 * x_2}$

If you can fill in values for all but one of the variables then you can solve for that variable.

Thanks, this really clarified it for me.