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The book I am reading has me doing the following.

Ft, M and V^2 are unknown values. I am trying to find V^2 by substituting one equation into the next, canceling the M's and solving for V^2. I might be making a couple of mistakes. I need to know what those mistakes are. Thanks.

Solve for Ft.

(Ft)(sin15)=(M)(V^2/R)

(Ft)=(M)(V^2/R)/sin15

Substitute Ft above into Ft below.

(Ft)(cos15)=(M)(G)

(M)((V^2/R)/sin15)(cos15)=(M)(G)

The M's cancel after division, I think.

(M)((V^2/R)/sin15)(cos15)/M=(M)(G)/M

((V^2/R)/sin15)(cos15)=(G)

Multiply V^2 on left to move it to the right.

((V^2)(V^2/R)/sin15)(cos15)=(G)(V^2)

(R/sin15)(cos15)=(G)(V^2)

Divide G on the right to move it to the left.

(R/sin15)(cos15)/G=(G)(V^2)/G

Now V^2 is isolated.

(R/sin15)(cos15)/G=V^2

6.8.jpg

Ft, M and V^2 are unknown values. I am trying to find V^2 by substituting one equation into the next, canceling the M's and solving for V^2. I might be making a couple of mistakes. I need to know what those mistakes are. Thanks.

Solve for Ft.

(Ft)(sin15)=(M)(V^2/R)

(Ft)=(M)(V^2/R)/sin15

Substitute Ft above into Ft below.

(Ft)(cos15)=(M)(G)

(M)((V^2/R)/sin15)(cos15)=

The M's cancel after division, I think.

(M)((V^2/R)/sin15)(cos15)/

((V^2/R)/sin15)(cos15)=(G)

Multiply V^2 on left to move it to the right.

((V^2)(V^2/R)/sin15)(cos15

(R/sin15)(cos15)=(G)(V^2)

Divide G on the right to move it to the left.

(R/sin15)(cos15)/G=(G)(V^2

Now V^2 is isolated.

(R/sin15)(cos15)/G=V^2

6.8.jpg

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Do the M's disappear the same way I divided them away?

I must say I have something to learn about how to get rid of the R. It is confusing to see a fraction inside of another fraction. It looks like you multiplied it by sin15

V^2 Cos15 / (R * sin15) = G

and that made the R disappear from the left. and of course it's multiplied on the right, that part makes since to me.

It looks like you multiplied (Cos15/Sin15) to move it to the right. Shouldn't that be divided to the right? Thanks.

(M)((V^2/R)/sin15)(cos15)=

V^2 Cos15 / (R * sin15) = G

V^2 (Cos15/Sin15)= GR

V^2 = GR* (Sin15 / Cos15) = GR Tan15

Multiply V^2 on left to move it to the right.

((V^2)(V^2/R)/sin15)(cos15

I think your mistake is this step.

Multiplying things with V^2 doesn't cancel it on the left side, it rather gives

((V^4)/R/sin15)(cos15)=(G)

If you want to isolate V^2 you can do it like this:

That's the start:

((V^2/R)/sin15)(cos15)=(G)

Simplify things a bit

(V^2*cos15)/(R*sin15)=G

Divide by cos15:

V^2/(R*sin15)=G/cos15

Multiply by R*sin15:

V^2=(G*R*sin15)/cos15

This trick is applicable when equations contain the same things (which are to be eliminated) on the same sides. If you try it conventionaly then you'd define Ft either from the first equation, by moving the sin15 to the denominator on the other side, and then place this rather cumbersome term into the left hand side of the second equation and then start eliminating. Alternatively one uses the second equation by moving the cos15 to the other side and substituting the Ft into the left hand side of the first equation. Less cumbersome as before, but still a lot of work. Dividing the two equations is far easier, since Ft divides into Ft and m into m.

HTH

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Start your 7-day free trialDivide the first equation by m sin 15°, thus F_t / m = v^2 / ( r sin 15°)

Divide the second equation by m cos 15°, thus F_t / m = g / cos 15°.

You have two equations F_t / m = ..., hence you can equate the right hand sides:

v^2 / ( r sin 15°) = g / cos 15°

Multiplication with r sin 15° preoduces

v^2 = r sin 15° g / cos 15°

(and once again use sin 15° / cos 15° = tan 15°)

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(M)((V^2/R)/sin15)(cos15)=

V^2 Cos15 / (R * sin15) = G

V^2 (Cos15/Sin15)= GR

V^2 = GR* (Sin15 / Cos15) = GR Tan15