Explain why applying different forces to objects of different masses result in different accelerations

[helloword365]

Homework Statement

This is the question:
If the standard body of 1 kg has an acceleration of magnitude a (in meters per second per second), then the force (in newtons) producing the acceleration has a magnitude
equal to a. We now have a workable definition of the force unit.

Explain why applying different forces (N) to objects of different masses result in different accelerations.

Relevant Equations

NA

I don't really get why applying different forces to objects of different masses would result in different accelerations. I read my textbook, and I understand the formula F(net) = m*a, and I think the reason may be because mass is inversely proportional to acceleration ? But this doesn't really explain why the unit force and acceleration are the same.

 

[anuttarasammyak]

Explain why applying different forces (N) to objects of different masses result in different accelerations.

A counter example. 2 N force applying 2 kg mass and 1 N force applying 1 kg mass result in same acceleration of 1 m/s^2.

 

[helloword365]

Hi, thanks for the counterexample, but how does this explain that different forces to different masses result in different accelerations?

 

[anuttarasammyak]

The counterexample shows that different forces to different masses do not have to result in different accelerations.

$$a=\frac{F}{m}$$

We can choose F and m as we wish. Their ratio F/m decides acceleration.

 

[kuruman]

Hi, thanks for the counterexample, but how does this explain that different forces to different masses result in different accelerations?

Imagine single force $\mathbf F$ acting on mass $m$ on a frictionless surface. Let $\mathbf a$ be the acceleration of the mass. Now look at the figure below.
The figure on the left shows a bird's eye view of two such identical masses being acted upon by identical forces $\mathbf F$. They have identical accelerations $\mathbf a$ and are started from rest at the same time.

Since the accelerations of the two masses are the same, they move as one. This means that they can be glued together and nothing changes. This is shown in the figure below, middle.

Well, what do we have here? It is shown in the figure below, right. We have mass $2m$ acted upon by total force $2\mathbf F$ having acceleration $\mathbf a.$ Clearly, for constant acceleration, if one doubles the mass one has to double the net force. In terms of an equation $$\mathbf a=\frac{\mathbf F_{\text{net}}}{m}.$$

 

[Lnewqban]

Explain why applying different forces (N) to objects of different masses result in different accelerations.

Isn't this question allowing too many variables at once?
It seems to me that it should be:

"Explain why applying different forces (N) to a standard body of 1 kg mass result in different accelerations."
or
"Explain why applying same force (N) to objects of different masses result in different accelerations."

As a matter of fact, applying different forces (N) to objects of different masses may very well result in similar accelerations.

If the magnitude of the applied force increases or decreases at the same rate than the magnitude of the mass does, there is no reason to observe any change in the magnitude of the resulting acceleration.

 

[PeroK]

Explain why applying different forces (N) to objects of different masses result in different accelerations.

This is a truly bizarre question. It can be rephrased as "why are all accelerations not of the same magnitude?"

Given that a force of zero produces zero acceleration, the question becomes "explain why non-zero acceleration is possible".

 

[DrJohn]

If f=ma, then a = f/m

Open a couple of books several times - say five for each book - and write down the page numbers you see for each book (simple but by no means perfect) random number generation.
Now insert the numbers into the equation using those from the first book as f and those from the second book as m.

Do you get the same number every time for a the acceleration, or does its value vary depending on the numbers you use?
Question solved.

 

[helloword365]

Imagine single force $\mathbf F$ acting on mass $m$ on a frictionless surface. Let $\mathbf a$ be the acceleration of the mass. Now look at the figure below.
The figure on the left shows a bird's eye view of two such identical masses being acted upon by identical forces $\mathbf F$. They have identical accelerations $\mathbf a$ and are started from rest at the same time.

Since the accelerations of the two masses are the same, they move as one. This means that they can be glued together and nothing changes. This is shown in the figure below, middle.

Well, what do we have here? It is shown in the figure below, right. We have mass $2m$ acted upon by total force $2\mathbf F$ having acceleration $\mathbf a.$ Clearly, for constant acceleration, if one doubles the mass one has to double the net force. In terms of an equation $$\mathbf a=\frac{\mathbf F_{\text{net}}}{m}.$$
View attachment 349409

hi, thank you! This makes a lot of sense.

 

[helloword365]

Isn't this question allowing too many variables at once?
It seems to me that it should be:

"Explain why applying different forces (N) to a standard body of 1 kg mass result in different accelerations."
or
"Explain why applying same force (N) to objects of different masses result in different accelerations."

As a matter of fact, applying different forces (N) to objects of different masses may very well result in similar accelerations.

If the magnitude of the applied force increases or decreases at the same rate than the magnitude of the mass does, there is no reason to observe any change in the magnitude of the resulting acceleration.

thank you as well :). And to everyone too as well in this thread. (just reading through them, one by one.)