Interactions of Momentum and Energy Principles
Created by Anya Kohnke
The Main Idea
When looking at the Momentum and Energy Principles, it is easy to find connections in the ways they are used. Both make it possible to predict and explain a range of real-world phenomena. These principles are so useful because they apply in every situation no matter the circumstances. The two principles can be used in conjunction with each other and to solve for the same quantities based on what information is provided.
The Momentum Principle restates and extends Newton's first law of motion to say that the change in momentum of a system is equal to the net force acting on the system times the duration of the interaction.
The Energy Principle states that the energy inputs from the surroundings may be positive or negative, corresponding to flows of energy from surroundings to system or from system to surroundings.
Both principles are fundamental principles because: They apply to every possible system, no matter how large or small or fast the system is. They are true for any kind of interaction. They relate an effect to a cause.
A Mathematical Model
The Momentum Principle is modeled
dP=Fnet*dt
The Energy Principle is modeled
dE=Wsurr=Fnet*dx
Examples
A robot spacecraft lands on an asteroid, picks up a sample, and blasts off to return to Earth; its total mass is 1500 kg. When it is 200 km from the center of the asteroid, its speed is 5 m/s and the rockets are turned off. At the moment when it has coasted to a distance 500 km from the center of the asteroid, its speed has decreased to 4.1 m/s. Calculate the mass of the asteroid.
Initial state: Rockets off, 5 m/s, 200 km from center of asteroid. Asteroid at rest. Final state: Speed 4.1 m/s, 500 km for center of asteroid.
Ef=Ei+W
Mc^c+KM+mc^2+Km+Uf=Mc^2+KM+mc^2+Km+Ui+W
Km+Uf=Km+Ui+0((1/2)mv^2)+(-GMm/r)=((1/2)mv^2)+(-GMm/r)
GM((1/r)-(1/r))=(1/2)(v^2-v^2)
M=2e16 kg
Connectedness
These principles connect with each other to solve problems.
History
Both of these principles have separately been tested, and through various observations and experiments involving large and small objects, moving slowly or at speeds near the speed of light, have proven themselves to stand under any circumstance.
See also
Newton's Second Law: the Momentum Principle
Further reading
Matter and Interactions by Ruth W. Chabay and Bruce A. Sherwood
External links
References
Matter and Interactions by Ruth W. Chabay and Bruce A. Sherwood