Mapertius's Principle and 2nd Newton's law

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Hi, I have been working on deriving the second Newton's law from the Mapertius principle applied to a perfectly elastic collision from a free fall acceleration problem. These are my calculations, but I keep getting a coefficient of 2 in my final answer for some reason. Could someone explain to me what I am doing wrong?

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I appreciate any help you can provide!
 

1. What is Mapertius's Principle?

Mapertius's Principle states that the total work done on a system is equal to the change in its kinetic energy. In other words, the work-energy principle states that the work done on an object is equal to the change in its kinetic energy.

2. What is Newton's 2nd Law?

Newton's 2nd Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be expressed as F = ma, where F is the net force, m is the mass of the object, and a is the acceleration.

3. How are Mapertius's Principle and Newton's 2nd Law related?

Mapertius's Principle and Newton's 2nd Law are related through the concept of work and energy. Mapertius's Principle is essentially a statement of the work-energy theorem, which is derived from Newton's laws of motion. Both principles help us understand the relationship between forces, work, and energy in a system.

4. Can Mapertius's Principle and Newton's 2nd Law be applied to all systems?

Yes, Mapertius's Principle and Newton's 2nd Law are fundamental principles of physics that can be applied to a wide range of systems, from simple objects moving in a straight line to complex systems involving multiple interacting objects. These principles provide a powerful framework for analyzing the motion and behavior of objects in various situations.

5. What are some real-world examples of Mapertius's Principle and Newton's 2nd Law in action?

Some common examples of Mapertius's Principle and Newton's 2nd Law in action include a car accelerating on a road, a ball falling under the influence of gravity, and a pendulum swinging back and forth. In each of these cases, the principles of work, energy, and force play a crucial role in determining the motion and behavior of the objects involved.

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