Problems with Newton's Second Law

In summary, the acceleration of a car being pushed by a constant force will decrease in relation to the mass of the car. The graph of acceleration on the y-axis and (1/m) on the x-axis will either be linear, parabolic, or exponential, depending on the formula used to relate mass and acceleration. The slope of the graph will indicate the type of relationship between mass and acceleration, whether it is a straight line, parabolic curve, or exponential curve. Further analysis is needed to determine the exact formula and type of graph.
  • #1
TheShehanigan
8
0

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.
 
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  • #2
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.
 
  • #3




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.
 

What is Newton's Second Law?

Newton's Second Law, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be.

What are some problems with Newton's Second Law?

There are several problems with Newton's Second Law, including:

  • The law assumes that the object is moving in a straight line with constant acceleration, which is not always the case in real-world scenarios.
  • The law does not take into account other factors that may affect an object's motion, such as air resistance or friction.
  • It is difficult to accurately measure and quantify all the forces acting on an object, making it challenging to apply the law in practical situations.

How does Newton's Second Law relate to Newton's First and Third Laws?

Newton's First Law, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. Newton's Second Law can be seen as an extension of this, as it explains how an object's motion changes when a force is applied to it. Newton's Third Law states that for every action, there is an equal and opposite reaction, which can also be applied to understanding the forces involved in Newton's Second Law.

Are there any exceptions to Newton's Second Law?

While Newton's Second Law is a fundamental principle in classical mechanics and holds true in most situations, there are a few exceptions. For example, at very high velocities approaching the speed of light, the law does not accurately predict the behavior of objects. Additionally, in the microscopic world of quantum mechanics, the law does not apply and a different set of principles are used to describe the motion of particles.

How is Newton's Second Law used in real-world applications?

Despite its limitations, Newton's Second Law is still widely used in various fields such as engineering, physics, and sports. It is used to calculate the acceleration, velocity, and displacement of objects in motion, and is the basis for designing vehicles, structures, and machines. In sports, it is used to analyze and improve techniques, such as in the development of faster and more efficient running techniques for sprinters.

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