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Консультация № 104222
04.10.2007, 00:46
0.00 руб.
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1. С какой скоростью должен вращаться шарик внутри гладкой сферы радиуса R=50см, чтобы все время оставаться в горизонтальной плоскости на высоте h=20 см от нижней точки сферы.
2. Искусственный спутник, используемый в системе телесвязи, запущен в плоскости земного экватора так, что все время находится в зените одной и той же точки шара. Во сколько раз радиус спутника R больше радиуса Земли R0 ? Считать известным радиус Земли R0 и ускорение свободного падения у поверхности Землию
2. Искусственный спутник, используемый в системе телесвязи, запущен в плоскости земного экватора так, что все время находится в зените одной и той же точки шара. Во сколько раз радиус спутника R больше радиуса Земли R0 ? Считать известным радиус Земли R0 и ускорение свободного падения у поверхности Землию
Обсуждение
Неизвестный
04.10.2007, 01:19
общий
это ответ
Здравствуйте, Timon!
1)Построим треугольник из радиуса, по которому вращается шарик, радиуса сферы, проведенного из центра сферы к шарику, и расстояния между центрами сферы и окружности вращения(0,5-0,2=0,3).
Шарик все время будет оставаться в горизонтальной плоскости на высоте h=20 см от нижней точки сферы, в том случае, если вертикальная составляющая центробежной силы будет >= силы тяжести.
Fц>=mv^2/R(0.5)
sina(a - угол между радиусами сферы и радиусом обращения шарика)=3/5
Fцsina>=mg
mv^2/Rsina>=mg
v>=sqrt(gRsina)=1.55 m/c
2)Cкорость обращения спутника на орбите Земли V=sqrt(gR)
Скорость вращения Земли U=2πR0/T(сутки)
Для выполнения поставленного условия V=U
2πR0/T=sqrt(gR)
R=(2πR0/T)^2/g
R/R0=[(2π/T)^2]*R0/g
1)Построим треугольник из радиуса, по которому вращается шарик, радиуса сферы, проведенного из центра сферы к шарику, и расстояния между центрами сферы и окружности вращения(0,5-0,2=0,3).
Шарик все время будет оставаться в горизонтальной плоскости на высоте h=20 см от нижней точки сферы, в том случае, если вертикальная составляющая центробежной силы будет >= силы тяжести.
Fц>=mv^2/R(0.5)
sina(a - угол между радиусами сферы и радиусом обращения шарика)=3/5
Fцsina>=mg
mv^2/Rsina>=mg
v>=sqrt(gRsina)=1.55 m/c
2)Cкорость обращения спутника на орбите Земли V=sqrt(gR)
Скорость вращения Земли U=2πR0/T(сутки)
Для выполнения поставленного условия V=U
2πR0/T=sqrt(gR)
R=(2πR0/T)^2/g
R/R0=[(2π/T)^2]*R0/g
Форма ответа
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