Finding Acceleration with Unknown Force & Mass

[mcdowellmg]

Homework Statement

"A certain force gives an object of mass m1 an acceleration of 12.2 m/s^2 and an object of mass m2 an acceleration of 4 m/s^2. What acceleration would the force give to an object of mass m2-m1, and also of an object of mass m2+m1?"

Homework Equations

acceleration = force/mass

The Attempt at a Solution

I deduced that a = F/(m2-m1). From there, I calculated that a*m2 = a*m1, because the F is the same throughout. I worked a little algebra...4*m2 = 12.2*m1, so 4/12.2*m2 = m1. That means that m1 is .32787 of m2, and thus m2 - m1 would leave an "m3" that is .67213 of m2. I tried to apply this to the acceleration by calculating .67213*4...getting an acceleration of 2.7, but that would mean m3 is greater than m2 in mass...which could not be possible. I guess I am getting a little lost in my own (il)logic. Any ideas?

Thanks!

 

[tiny-tim]

welcome to pf!

hi mcdowellmg! welcome to pf!

(try using the X² and X₂ icons just above the Reply box )

I deduced that a = F/(m2-m1).

uhh? what is a?

start again, and first convert the following words into two equations:

"A certain force gives an object of mass m1 an acceleration of 12.2 m/s^2 and an object of mass m2 an acceleration of 4 m/s^2.

 

[mcdowellmg]

a is acceleration, sorry!

12.2*m1 = F and 4*m2 = F, so I know that 12.2*m1 = 4*m2, because F is the same throughout. After that, I'm stuck...and frustrated!

Thanks!

 

[HallsofIvy]

a is acceleration, sorry!

12.2*m1 = F and 4*m2 = F, so I know that 12.2*m1 = 4*m2, because F is the same throughout. After that, I'm stuck...and frustrated!

Thanks!

So m1= F/12.2 and m2= F/4. Now m1- m2= F/12.2- F/4= F/?

 

[mcdowellmg]

m2-m1 = F/8.2 ?

Am I not able to get an actual number?

 

[tiny-tim]

look at the question!

it doesn't ask for m₂ - m₁, it only asks for the acceleration of such a mass

which is … ?

 

[mcdowellmg]

Oops! So it is as simple as subtracting the accelerations to get 8.2? I find that hard to believe! I guess I made it too complicated. Thanks.

 

[tiny-tim]

yes and no

unfortunately, your previous equation was wrong …

So m1= F/12.2 and m2= F/4. Now m1- m2= F/12.2- F/4= F/?

m2-m1 = F/8.2

try it again …

carefully! ​