Word Problem

[vanbeersj]

I have difficuties arranging the equations in word problems, for example in this question:

In a certain roller mechanism, the radius of one steel ball is 2.00 cm greater than the radius of a second steel ball. If the difference in their masses is 7100g, find the radii of the balls. The density of steel is 7.70 g/cm^3

ok so I came up with R1+2.0cm= R2 and m1-m2=7100g. I know V=m/d and that V=4/3 pie r^3, I can equate these two equations but I still cannot solve for just one variable. I'm not sure how to proceed.

 

[fasteddie65]

In a certain roller mechanism, the radius of one steel ball is 2.00 cm greater than the radius of a second steel ball. If the difference in their masses is 7100g, find the radii of the balls. The density of steel is 7.70 g/cm^3

The mass of an object is its volume multiplied by its density.
The volume of a sphere is (4/3)(pi)r^3.

This should help you get the equations.

 

[chivox]

Re: Finding the radii of two steel balls

I have difficuties arranging the equations in word problems, for example in this question:

In a certain roller mechanism, the radius of one steel ball is 2.00 cm greater than the radius of a second steel ball. If the difference in their masses is 7100g, find the radii of the balls. The density of steel is 7.70 g/cm^3

ok so I came up with R1+2.0cm= R2 and m1-m2=7100g. I know V=m/d and that V=4/3 pie r^3, I can equate these two equations but I still cannot solve for just one variable. I'm not sure how to proceed.

When the problem says "is" or one of those "to be" verbs, THAT is where you put the equal sign.

... the radius of one steel ball is 2.00 cm greater than the radius of a second steel ball ...

becomes

R1 = 2 + R2

Then, since you know m1 - m2 = 7100, can you write the expression that represents the mass of sphere 1 and the expression that represents the mass of sphere 2? That would get you started.

 

[Deleted member 4993]

I have difficuties arranging the equations in word problems, for example in this question:

In a certain roller mechanism, the radius of one steel ball is 2.00 cm greater than the radius of a second steel ball. If the difference in their masses is 7100g, find the radii of the balls. The density of steel is 7.70 g/cm^3

ok so I came up with R1+2.0cm= R2 and m1-m2=7100g. I know V=m/d and that V=4/3 pie r^3, I can equate these two equations but I still cannot solve for just one variable. I'm not sure how to proceed.

Okay - you have named the variables to be found r_1 and r_2

You know

\(\displaystyle r_1 \, - \, r_2 \, = 2\)

\(\displaystyle M_1 \, - \, M_2 \, = 7100\)

\(\displaystyle \frac{M_1 \, - \, M_2}{Density} \, = \frac{7100}{7.7} \, = 922.08\)

Then

\(\displaystyle V_1 \, - \, V_2 \, = 922.08\)

\(\displaystyle r_1^3 \, - \, (r_1 - 2)^3 \, = \frac{3}{4\pi}\cdot 922.08\)............One equation and one unknown