How Does Subtracting and Adding Masses Affect Acceleration in a Force Equation?

[mcdowellmg]

Homework Statement

A certain force gives an object of mass m1 an acceleration of 11.9 m/s^2 and an object of mass m2 an acceleration of 2.8 m/s^2. What acceleration would the force give to an object of mass

m2 - m1

and

m2 + m1?

Homework Equations

F=ma
Force = mass*acceleration

The Attempt at a Solution

I know that a = F/(m2-m1).
11.9*m1 = F and 2.8*m2 = F, so I know that 11.9*m1 = 2.8*m2, because F is the same throughout.
Therefore, m1= F/11.9 and m2= F/2.8. Now m1- m2= F/11.9- F/2.8= -0.273109F.
This would lead me to believe that -0.273109F = m1-m2, so if a=F/(m2-m1), then a should be F/-0.273109F, which is -3.661.

However, that is not coming up as correct. I haven't attempted the m2+m1 mass, because I am trying to figure out the first one, and when I do, it should be easy to compute.EDIT- Well, never mind. Apparently, it was 3.66, without the negative. Where did I go wrong with the negative?

 

[Andrew Mason]

Homework Statement

A certain force gives an object of mass m1 an acceleration of 11.9 m/s^2 and an object of mass m2 an acceleration of 2.8 m/s^2. What acceleration would the force give to an object of mass

m2 - m1

and

m2 + m1?

Homework Equations

F=ma
Force = mass*acceleration

The Attempt at a Solution

I know that a = F/(m2-m1).
11.9*m1 = F and 2.8*m2 = F, so I know that 11.9*m1 = 2.8*m2, because F is the same throughout.
Therefore, m1= F/11.9 and m2= F/2.8. Now m1- m2= F/11.9- F/2.8= -0.273109F.
This would lead me to believe that -0.273109F = m1-m2, so if a=F/(m2-m1), then a should be F/-0.273109F, which is -3.661.

Start with:

$$F/a_1 = m_1 \text{ and } F/a_2 = m_2$$

From that work out m2-m1 and m1+m2 in terms of F, a1 and a2. Then find the accelerations for m2-m1 and m2+m1

AM

 

[rl.bhat]

In the problem they have asked the acceleration of m2 - m1 which is equal to 3,661 m/s^2

 

[Lostinthought]

Start with:

$$F/a_1 = m_1 \text{ and } F/a_2 = m_2$$

From that work out m2-m1 and m1+m2 in terms of F, a1 and a2. Then find the accelerations for m2-m1 and m2+m1

AM

the -0.273109F u got is m1-m2,and u used it as m2-m1 to find the acceleration.its just a careless error noting more

 

[rwisz]

Your approach to solving the problem is correct, but there is a mistake in your final calculation. When you substitute the values for m1 and m2 into the equation a = F/(m2-m1), you should get a = F/(-0.273109F). The negative sign should be in the denominator, not in front of the entire fraction. This gives you a = -3.66 m/s^2, which is the correct answer.

For the m2+m1 mass, you can follow the same approach and substitute the values for m1 and m2 into the equation a = F/(m2+m1). This will give you a = F/(14.7m).