Problems with Newton's Second Law

[TheShehanigan]

Homework Statement

Given a car being pushed by a constant force:

a. How will the acceleration change in relation to the mass of the car? --> Done, it'll decrease
b. How will a graph of acceleration in the y-axis and and (1/m) being the x-axis will look like? What will the slope of the graph mean? --> Trouble with this one

Homework Equations

F = ma
a = F(1/M)

The Attempt at a Solution

For part B, I have already determined the graph should be decreasing, but I have doubts if it's exponential or as (1/x) does. I think it's as (1/x), since F is constant. As to what the slope means, I think it refers to the Inertia of the object in question. I have serious doubts with this though.

Any help is greatly appreciated.

 

[Delphi51]

a. How will the acceleration change in relation to the mass of the car? --> Done, it'll decrease

I don't care for this answer, which is an oversimplification! In my opinion, the question asks for a "relationship" between mass and acceleration. That word "relationship" means they want the formula relating mass and acceleration. You probably have a formula with an "m" and an "a" in it. The thing to do is rearrange it so it says "a = ...".

For the b part, compare your formula for a= with the some standard formulas.
For example, y = slope*x + b is the formula for a straight line.
y = a*x^2 is a quadratic or parabola
y = a*e^x is an exponential.
Which one fits your formula for "a=" . . . with the "y" replaced by "a", the "x" replaced by "1/m" ?
You should find that it is one of the above, exactly, so you will know whether the graph is linear, parabolic or exponential.

 

[nlightner]

There are a few potential problems with using Newton's Second Law to analyze this situation. First, the law assumes that the force acting on an object is constant, which may not be the case in this scenario. If the person pushing the car applies varying amounts of force, the acceleration may not follow a predictable pattern.

Secondly, the law assumes that the mass of the object is constant, which may not be true in this situation. If the car has items inside of it that can move around, the mass of the car may change, affecting the acceleration.

As for part B, it is important to note that the equation a = F(1/M) is only valid for objects with constant mass. In this situation, the mass of the car is not constant, so this equation may not accurately represent the relationship between acceleration and mass. Additionally, the graph of acceleration versus (1/m) may not be a straight line, as the relationship between these variables may be more complex.

In terms of the slope of the graph, it may not necessarily represent the inertia of the object. The slope of a graph typically represents the rate of change between the two variables, so in this case, it may represent the rate at which the acceleration changes as the mass of the car changes. However, without knowing the specific values and units of the variables, it is difficult to accurately interpret the slope of the graph.

In conclusion, while Newton's Second Law is a useful tool for analyzing many situations, it may not be applicable or accurate in all cases. It is important to consider the limitations and potential issues with using this law in any scientific analysis.