How to find the acceleration of 2 objects under same force

[~christina~]

Homework Statement

A force F to an object m1 produces an acceleration of 3m/s^2. The same force is applied to a second object of mass m2 produces an acceleration of 1.00m/s^2

a.) value ratio of m1/m2

b.) If m1 and m2 are combined into 1 object, what is the acceleration under the action of force $$\vec{} F$$?

Homework Equations

F=ma

The Attempt at a Solution

a.) m1/m2= a2/a1

m1/m2= 1.00m/s^2/ 3.00m/s^2


b.) for b I'm not sure what they mean by combine the masses but m1 + m2 = ?

I'm not sure if I can just combine the accelerations since they are vector quantities but mass is scalar so it can be combined...


I need help with part b.

Thanks

 

[Gale]

For part a, don't forget that the units cancel out.
For part b, solve for m1 and m2 in terms of F. Then you put (m1+m2) in terms of F, which you plug back into F=ma, then solve for a.

 

[~christina~]

well for part
a) m1/m2= .333

b) F= m1(3.00m/s^2)
m1= F/(3.00m/s^2)
F= m2(1.00m/s^2)
m2= F/(1.00m/s^2)

m1 + m2= F/(3.00m/s^2) + F/ (1.00m/s^2) = F/(3.00m/s^2) + 3F/(3.00m/s^2) = 4F/(3.00m/s^2)

then if I did that right..I plug that into F=ma...

F=ma
F= 4F/3.00m/s^2 * a

3.00m/s^2(F)= 4F*a
a= (3.00m/s^2)(F)/4F

Is this fine??

 

[Gale]

The F's cancel, and its neater if you write 3/4 m/s^2, imo. But yes, that's right

 

[~christina~]

Oh..okay..Thank You =D