# Newton's Second Law vs. Energy Equations

In summary, the conversation discusses a test on kinetics and energy of moving particles with various types of problems. The two methods of solving problems in this realm are Newton's second law and energy equations, with the latter being more useful for problems involving velocities and displacements. However, energy conservation has its limitations and Newton's laws can be applied even in cases where energy conservation is not valid. Non-conservative forces, such as the normal force, air/water drag, and frictional forces, may also need to be considered in problem-solving.
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## Homework Statement

I'm taking a test next week on kinetics and energy of moving particles. Problems include things like sliding blocks, friction, braking automobiles, collars sliding on poles, springs, max/min heights/velocities, tensions, accelerations, etc...

We learned two ways of solving problems in the kinetics realm... Newton's second law and energy equations. When do I use one vs. the other?

## Homework Equations

Newton's 2nd Law
F=ma

PE=Potential Energy, KE=Kinetic Energy, SE=Spring Energy, Work could be from friction, drag, etc.

Energy Eqn
PE1+KE1+SE1+Work=PE2+KE2+SE2

## The Attempt at a Solution

My gut says that if the problem is asking for an acceleration or a normal force, F=ma needs to get involved. Otherwise, I may or may not need to use F=ma + the energy eqn.

We're using chapter 12/13 in Vector Mechanics for Engineers by Beer/Johnston 8th Ed.

Energy equations are extremely helpful when dealing with problems involving velocities and displacements. They however do not have an explicit time factor.
Energy methods are more useful when dealing with position varying forces,as in a two body system. I remember I tried to solve a two body problem using the force method here on pf and ended up scratching my head for a real long time. Gravitation problems are also easier to do using energy methods.
However energy conservation has its limitations-Newton's Laws do not have that problem.Being the more basic they are applicable even when energy conservation is flouted.
I think you would like to check the thread "Force method for two body systems" to see my point.

Thanks aim1732... I couldn't find the thread you referenced. Perhaps you could post the link here?

The "do not have an explicit time factor" part makes sense. My tutor said something about not being able to use the energy equations with "non-conservative" forces, like the normal force. What, besides the normal force, air/water drag, and frictional forces are non-conservative in everyday life?

You would encounter non-conservative forces that you mentioned plus some lesser known ones as the battery force that is responsible for maintaining potential difference across the terminals of a battery,and non elastic material stress. However it is worth noting that energy equations(as opposed to conservation of mechanical energy) are still valid and can be applied meaningfully for even non-conservative forces.

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As a scientist, it is important to understand the principles behind both Newton's Second Law and energy equations in order to solve problems in kinetics. Both of these approaches have their own advantages and can be used in different scenarios.

Newton's Second Law, F=ma, is a fundamental law of physics that relates the force applied on an object to its mass and acceleration. This approach is useful when the problem involves determining the acceleration or force acting on an object. It is also helpful in situations where there are multiple forces acting on an object and you need to determine the net force.

On the other hand, energy equations, such as PE=Potential Energy, KE=Kinetic Energy, SE=Spring Energy, and work, are useful when the problem involves determining the change in energy or the work done on an object. This approach is particularly helpful in problems involving conservation of energy, such as in the case of a swinging pendulum or a rollercoaster.

In general, if the problem is asking for information about forces or accelerations, Newton's Second Law is the most appropriate approach. If the problem involves determining the change in energy or work done on an object, then energy equations should be used. However, in some cases, it may be necessary to use both approaches in order to fully understand and solve the problem.

It is also important to note that both approaches are based on the same fundamental principles and are interconnected. For example, Newton's Second Law can be derived from energy equations, and energy equations can be derived from Newton's Second Law. Therefore, it is important to have a thorough understanding of both approaches in order to effectively solve problems in kinetics.

## 1. 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 it and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be, and the more massive the object is, the less it will accelerate.

## 2. What are the energy equations?

The energy equations, also known as the Work-Energy theorem, are a set of equations that relate the work done on an object to its change in kinetic and potential energy. The equations state that the net work done on an object is equal to the change in its kinetic energy plus the change in its potential energy.

## 3. How are Newton's Second Law and the energy equations related?

Newton's Second Law and the energy equations are both fundamental principles in classical mechanics that describe the behavior of objects in motion. The energy equations can be derived from Newton's Second Law, as they both involve the concept of work, force, and motion.

## 4. Can Newton's Second Law be applied to systems with energy transformations?

Yes, Newton's Second Law can be applied to systems with energy transformations. In these cases, the net force acting on the system may change due to the transformation of energy, but the overall principle of the law remains the same - the acceleration of an object is determined by the net force acting on it.

## 5. Which is more useful in solving real-world problems - Newton's Second Law or the energy equations?

Both Newton's Second Law and the energy equations are equally useful in solving real-world problems. The choice between the two depends on the specific problem being solved and the information available. In some cases, it may be more efficient to use Newton's Second Law, while in others, the energy equations may provide a more straightforward solution.

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