Physics, 24.05.2021 08:30 zania30

What is the baseball's mechanical energy when it is at a height of 8.0 m? Explain.

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In this section, we elaborate and extend the result we derived in Potential Energy of a System, where we re-wrote the work-energy theorem in terms of the change in the kinetic and potential energies of a particle. This will lead us to a discussion of the important principle of the conservation of mechanical energy. As you continue to examine other topics in physics, in later chapters of this book, you will see how this conservation law is generalized to encompass other types of energy and energy transfers. The last section of this chapter provides a preview.

The terms ‘conserved quantity’ and ‘conservation law’ have specific, scientific meanings in physics, which are different from the everyday meanings associated with the use of these words. (The same comment is also true about the scientific and everyday uses of the word ‘work.’) In everyday usage, you could conserve water by not using it, or by using less of it, or by re-using it. Water is composed of molecules consisting of two atoms of hydrogen and one of oxygen. Bring these atoms together to form a molecule and you create water; dissociate the atoms in such a molecule and you destroy water. However, in scientific usage, a conserved quantity for a system stays constant, changes by a definite amount that is transferred to other systems, and/or is converted into other forms of that quantity. A conserved quantity, in the scientific sense, can be transformed, but not strictly created or destroyed. Thus, there is no physical law of conservation of water.

Systems with a Single Particle or Object

We first consider a system with a single particle or object. Returning to our development of (Figure), recall that we first separated all the forces acting on a particle into conservative and non-conservative types, and wrote the work done by each type of force as a separate term in the work-energy theorem. We then replaced the work done by the conservative forces by the change in the potential energy of the particle, combining it with the change in the particle’s kinetic energy to get (Figure). Now, we write this equation without the middle step and define the sum of the kinetic and potential energies, K+U=E; to be the mechanical energy of the particle

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the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

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sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. these color-magnitude plots are known as hertzsprung–russell diagramsafter their co-developers, ejnar hertzsprungand henry norris russell. stars on this band are known as main-sequence stars or dwarf stars. these are the most numerous true stars in the universe, and include the earth's sun.after condensation and ignition of a star, it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. during this stage of the star's lifetime, it is located on the main sequence at a position determined primarily by its mass, but also based upon its chemical composition and age. the cores of main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of gravitational collapse from the overlying layers. the strong dependence of the rate of energy generation on temperature and pressure to sustain this balance. energy generated at the core makes its way to the surface and is radiated away at the photosphere. the energy is carried by either radiation or convection, with the latter occurring in regions with steeper temperature gradients, higher opacity or both.the main sequence is sometimes divided into upper and lower parts, based on the dominant process that a star uses to generate energy. stars below about 1.5 times the mass of the sun (1.5 m☉) primarily fuse hydrogen atoms together in a series of stages to form helium, a sequence called the proton–proton chain. above this mass, in the upper main sequence, the nuclear fusion process mainly uses atoms of carbon, nitrogen and oxygen as intermediaries in the cno cycle that produces helium from hydrogen atoms. main-sequence stars with more than two solar masses undergo convection in their core regions, which acts to stir up the newly created helium and maintain the proportion of fuel needed for fusion to occur. below this mass, stars have cores that are entirely radiative with convective zones near the surface. with decreasing stellar mass, the proportion of the star forming a convective envelope steadily increases. main-sequence stars below 0.4 m☉undergo convection throughout their mass. when core convection does not occur, a helium-rich core develops surrounded by an outer layer of hydrogen.in general, the more massive a star is, the shorter its lifespan on the main sequence. after the hydrogen fuel at the core has been consumed, the star evolves away from the main sequence on the hr diagram, into a supergiant, red giant, or directly to a white dwarf.

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What is the baseball's mechanical energy when it is at a height of 8.0 m? Explain....

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