Finding force on a third particle given final velocity and center of mass

[mr_joshua]

I am going brain dead! How do I convert force to velocity? I do know the acceleration and time and mass, but my conversion is not working in the problem. I am given the final Velocity-center of mass, but I need to find the Force in N for a third particle.

 

[Integral]

If you would give us a complete statement of the problem, we may be able to help you. What you have given us is insufficient to understand what you are doing or what you want.

 

[mr_joshua]

Here is the simple problem.

All of the objects start at rest and move for 32 sec. If the velocity of the center of mass after 32 sec is 6 m/s at an angle of 124, determine the magnitude and direction of mass 3.

m1---4kg----F1--1.8N @ 48
m2---5kg----F2--1.5N @ 245
m3---6kg----F3--?N @ ?

The answer I got was 2.671N @ 143.349

The answer in the book is 3.18N @ 132.4

I used vf=vi+at to find a...

then used Ma_cm= F1+F2+F3 broken into the x and y components

 

[Zorodius]

It sounds like you were on the right track. Perhaps your mistake was just in the evaluation?

The book's answer seems to have too many significant digits, considering that you were only given forces with two significant digits of accuracy.

You can use Newton's second law for components to get two equations with two variables,

$$F_{net x} = F_{1x} + F_{2x} + F_{3x} = M_{net} a_x$$
$$F_{net y} = F_{1y} + F_{2y} + F_{3y} = M_{net} a_y$$

Where

$$F_{3x} = F_3 \cos \theta$$

and

$$F_{3y} = F_3 \sin \theta$$

It would probably be easiest to solve for F3. Substitute that into the other equation, and you have something you can rearrange and evaluate, using the fact that

$$v_x = a_x t$$

and

$$v_y = a_y t$$

 

[Zorodius]

Do those all show up as "LaTeX graphic is being generated, please wait a moment, then reload the page" to anyone else? It looks fine when I preview it, but not when it's actually posted.

 

[Gaz031]

Do those all show up as "LaTeX graphic is being generated, please wait a moment, then reload the page" to anyone else? It looks fine when I preview it, but not when it's actually posted.

It appears the same for me.

 

[mr_joshua]

Thanks for the help. After looking at the problem again, I realized I used cos in both the x and y components. Silly stupid mistake. got the right answer now though.