Newton's Second Law Equation acceleration Question

[Slusho]

Homework Statement

A certain force gives object m₁ an acceleration of 12.0 m/s². The same force gives object m₂ an acceleration of 3.30 m/s². What acceleration would the force give to an object whose mass is (a) the difference between m₁ and m₂ and (b) the sum of m₁ and m₂.

Homework Equations

F=ma

The Attempt at a Solution

I found these two solutions online:
http://www.physforum.com/index.php?showtopic=6754
http://www.jiskha.com/display.cgi?id=1286634662
but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

Any help is greatly appreciated!

 

[azizlwl]

Which part that you do not understand.
Use the formula a=F/m.

 

[SammyS]

Homework Statement

A certain force gives object m₁ an acceleration of 12.0 m/s². The same force gives object m₂ an acceleration of 3.30 m/s². What acceleration would the force give to an object whose mass is (a) the difference between m₁ and m₂ and (b) the sum of m₁ and m₂.

Homework Equations

F=ma

The Attempt at a Solution

I found these two solutions online:
http://www.physforum.com/index.php?showtopic=6754
http://www.jiskha.com/display.cgi?id=1286634662
but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

Any help is greatly appreciated!

Hello Slusho. Welcome to PF !

What are those manipulations? What have you tried?

F = m₁a₁ and F = m₂a₂, where a₁ = 12.0 m/s² and a₂ = 3.30 m/s² .

Therefore, $\displaystyle m_1=\frac{F}{a_1}\text{ and } m_2=\frac{F}{a_2}\,.$ Correct?

Now, use all this with F = (m₁ + m₂)a₁₊₂ to find a₁₊₂ .

How's your algebra?

 

[Slusho]

I figured it out!

$$F=(\frac{F}{a_{1}}+\frac{F}{a_{2}})a_{1+2}$$
$$\frac{1}{a_{1+2}}=\frac{1}{F}(\frac{F}{a_{1}}+ \frac{F}{a_{2}})$$
$$\frac{1}{a_{1+2}}=\frac{1}{a_{1}}+\frac{1}{a_{2}}$$

Thank you so much for you help! I had to work it several ways for a good half hour until I did it correctly.

 

[Nickie]

I can provide a response to this question. First, let's review Newton's Second Law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be represented by the equation F=ma, where F is force, m is mass, and a is acceleration.

In this problem, we are given the same force acting on two different objects, m1 and m2, resulting in two different accelerations, 12.0 m/s2 and 3.30 m/s2, respectively. We are then asked to find the acceleration of a new object with a mass that is either the difference or the sum of m1 and m2.

To find the acceleration of an object with a mass that is the difference between m1 and m2, we can use the equation F=ma and substitute in the given values for force and mass. This gives us:

F = ma
F = (m1-m2)a

We also know that the force is the same for both objects, so we can set these two equations equal to each other:

(m1-m2)a = m1a

Solving for a, we get:

a = m1/(m1-m2)

Using the values given, we can plug in m1=12.0 m/s2 and m2=3.30 m/s2, giving us an acceleration of:

a = (12.0)/(12.0-3.30) = 1.57 m/s2

This means that an object with a mass that is the difference between m1 and m2 would have an acceleration of 1.57 m/s2 when acted upon by the same force.

To find the acceleration of an object with a mass that is the sum of m1 and m2, we can use a similar approach. Again, we start with the equation F=ma and substitute in the given values:

F = ma
F = (m1+m2)a

Setting these two equations equal to each other and solving for a, we get:

a = F/(m1+m2)

Using the values given, we can plug in m1=12.0 m/s2 and m2=3.30 m/s2, giving us an acceleration of:

a = (12.0)/(12.0+3.30) = 0.8 m/s2

This means