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| 1. |
derive the formula for force which depend upon mass and accleration of an object |
| Answer» According to Newton\'s Second Law: If a particle of mass\xa0{tex}m{/tex}\xa0has velocity\xa0{tex}v{/tex}\xa0at any moment\xa0{tex}t{/tex},{tex}\\vec{F}=\\frac{d\\vec{p}}{dt}{/tex}, where\xa0{tex}\\vec{F}{/tex}is the force and\xa0{tex}\\vec{p}=m\\vec{v}{/tex}\xa0is the momentum.Thus,{tex}\\vec{F}=\\frac{d(m{\\vec{v}})}{dt}=m\\frac{d\\vec{v}}{dt}+\\vec{v}\\frac{dm}{dt}{/tex}For cases where mass changes with time, the above equation would be applicable.Special Cases:\tIf mass remains constant, as we see in most theories an numericals,\xa0{tex}\\frac{dm}{dt}=0{/tex}\xa0hence,\xa0{tex}\\vec{F}=m\\frac{d\\vec{v}}{dt}=m\\vec{a}{/tex}, where\xa0{tex}\\vec{a}{/tex}\xa0is the acceleration of the object.\tIf the velocity remains constant but mass emerges out or gets added at a constant rate, as in cases of water coming out of hose pipe, or sands added at constant rate upon a moving belt;\xa0{tex}\\vec{F}=\\vec{v}\\frac{dm}{dt}{/tex}. | |