Fundamental Forces Problem: Acceleration from Planet

[JoeyBob]

Homework Statement

See attached

Relevant Equations

F=mg, F=-GmM/r^2

I know its something to do with my unit conversions because my answer is the right numbers but too small by a factor of 10000.

I convert the radius to meters by multiplying it by 1000. I convert the density to kg/m^3 by dividing it by 10.

I find the volume using the equation (4/3)*pi*radius^3

I find the mass by multiplying the volume by the density.

I find the force of gravity by using GMm/(radius planet+distance from planet)^2

(distance was also converted to m by multiplying it by 1000)

Fg=ma, the small masses cancel.

I get an answer that has the right numbers but is too small by a factor of 10000.

 

[hmmm27]

Try to solve it again, explicitly including units of measurement in the equation. Post your work if it doesn't come out right.

 

[TSny]

Homework Statement:: See attached
Relevant Equations:: F=mg, F=-GmM/r^2

I convert the radius to meters by multiplying it by 1000.

OK

I convert the density to kg/m^3 by dividing it by 10.

But the density is already given in kg/m³.

I find the volume using the equation (4/3)*pi*radius^3

I find the mass by multiplying the volume by the density.

I find the force of gravity by using GMm/(radius planet+distance from planet)^2

OK. Wouldn't the result of this calculation give you the answer to the problem. I don't see why you went on to write the following:

Fg=ma, the small masses cancel.

It could be that you are making one or more errors that we can't see. It will help if you show the full calculation with the particular numbers and units that you used.

 

[JoeyBob]

OK

But the density is already given in kg/m³.OK. Wouldn't the result of this calculation give you the answer to the problem. I don't see why you went on to write the following:It could be that you are making one or more errors that we can't see. It will help if you show the full calculation with the particular numbers and units that you used.

I screenshotted the wrong question... here's the right one.

Caluclutations:

3.93/10=0.393

Mass=Volume*density

Mass=(4/3)*pi*3390000^3*0.393=6.4133*10^19

F=Gmm/r^2

=6.67*10^-11*6.4133*10^19m/(3390000+171900)^2

=0.000337166ma=ma

a=0.00033716

 

[TSny]

Caluclutations:

3.93/10=0.393

The conversion here is wrong. Think about the fact that the cm is cubed. Otherwise, your work looks good to me.

 

[JoeyBob]

The conversion here is wrong. Think about the fact that the cm is cubed. Otherwise, your work looks good to me.

To convert cm cubed to m cubed don't you divide by 100 (since its divided by you multiply). There are 1000 g in a kg, so you divide by 1000. 100/1000 means you divide by 10.

 

[TSny]

To convert cm cubed to m cubed don't you divide by 100 .

No. Consider a simpler example where you can draw a picture. There are 3 ft in a yd. How many ft³ are in 1 yd³. Sketch a cube with each edge 1 yd. How many ft³ will fit into that cube?

 

[JoeyBob]

No. Consider a simpler example where you can draw a picture. There are 3 ft in a yd. How many ft³ are in 1 yd³. Sketch a cube with each edge 1 yd. How many ft³ will fit into that cube?

So you multiple it by 1000 since its cubed?

 

[TSny]

So you multiple it by 1000 since its cubed?

I'm not sure what "it" refers to here. You might be right.

To convert 5 cm³ to m³ you would not multiply the 5 by 1000.

But if you mean that to convert g/cm³ to kg/m³ you multiply by 1000, then yes!

 

[JoeyBob]

I'm not sure what "it" refers to here. You might be right.

To convert 5 cm³ to m³ you would not multiply the 5 by 1000.

But if you mean that to convert g/cm³ to kg/m³ you multiply by 1000, then yes!

Thats so dumb. Thanks for the help.