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From page 187: “In ordinary language, conserving energy means trying not to waste useful energy resources. In the scientific meaning of conservation, energy is always conserved no matter what happens.” Conservation of energy is one of the few universal principles of physics. No exception has ever been found.
- Chapter 13 Energy, Kinetic Energy, and Work
- 13.1 The Concept of Energy and Conservation of Energy
- 13.3.1 Constant Accelerated Motion
- Example 13.2 Work Done by Static Fiction
- 13.8 Work and the Scalar Product
- 13.8.2 Kinetic Energy and the Scalar Product
- Δx = Δxö i . Note that Δx = Δxö
- f = −μ
- Example 13.13 Work done by the Inverse Square Gravitation Force
Acceleration of the expansion of the universe is one of the most exciting and significant discoveries in physics, with implications that could revolutionize theories of quantum physics, gravitation, and cosmology. With its revelation that close to the three-quarters of the energy density of the universe, given the name dark energy, is of a new, unk...
The transformation of energy is a powerful concept that enables us to describe a vast number of processes: Falling water releases stored gravitational potential energy, which can become the kinetic energy associated with a coherent motion of matter. The harnessed mechanical energy can be used to spin turbines and alternators, doing work to generate...
Let’s consider a constant accelerated motion of a rigid body in one dimension in which we treat the rigid body as a point mass. Suppose at t = 0 the body has an initial x -component of the velocity given by v . If the acceleration is in the direction of the x,i displacement of the body then the body will increase its speed. If the acceleration is o...
Suppose you are initially standing and you start walking by pushing against the ground with your feet and your feet do not slip. What is the work done by the static friction force acting on you? Solution: When you apply a contact force against the ground, the ground applies an equal and opposite contact force on you. The tangential component of thi...
We shall introduce a vector operation, called the scalar product or “dot product” that takes any two vectors and generates a scalar quantity (a number). We shall see that the physical concept of work can be mathematically described by the scalar product between the force and the displacement vectors.
For an object undergoing three-dimensional motion, the velocity of the object Cartesian components is given by v = v ö ö + v j + v y z in . Recall that the magnitude of vector is given by the square root of the scalar product of the vector with itself, a
i is the component of the displacement and hence can be greater, equal, or less than zero (but is shown as greater than zero in the figure for clarity). The scalar product between the force vector F and the displacement vector Δx is
kmgcosθö i , and FN = mgcosθö Fg = mgsinθ ö i − mgcosθö j, j . The work done by the normal force is zero because the normal force is perpendicular the displacement W N = FN ⋅ Δr = mgcosθö j⋅l ö i = 0. Then the work done by the friction force is negative and given by W f = F
Consider a body of mass m in moving in a fixed orbital plane about the sun. The mass of the sun is m s . How much work does the gravitation interaction between the sun and the body done on the body during this motion? Solution: Let’s assume that the sun is fixed and choose a polar coordinate system with the origin at the center of the sun. Initiall...
It leads to the answer what energy is and why it is conserved, describes the origin and meaning of entropy, and derives the set of energy forms and shows the general systematics behind the ...
Whenever an object moves up against gravity or a spring is compressed, energy is stored in what we call potential energy. Since we have conservation of mechanical energy, which is the sum of the potential and kinetic energies, this stored energy can later be used to generate, or be transferred to, kinetic energy.
To summarize this section, the visualization technique of drawing energy bar graphs can be applied to systems in which mechanical energy is conserved, or even to systems when it is not conserved. Drawing these bar graphs is a good way to keep track of the different types of energy in a system.
We would not exist without the energy radiated by the sun, which is liberated there by its nuclear reactions. The state of each atom and molecule is characterized by its internal energy, that is, by the motion of its components and by their distribution in space and the resulting electric potential energy.
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Conservation of Energy in order to analyze the change of state of a system. Definition: Change of Energy The total change in energy of a system and its surroundings between the final state and the initial state is zero, ∆=EEtotal ∆system +∆Esurroundings =0 (D.1.1)
