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Консультация № 173602
23.10.2009, 12:29
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Шар скатывается с наклонной плоскости высоты h.начальная скорость тела=0.Определить скорость тел у основания наклонной плоскости,время скольжения,учесть что скатывание идет без скольжения
Обсуждение
27.10.2009, 23:51
общий
это ответ
Здравствуйте, Diesel13.
В начальный момент времени шар обладает потенциальной энергией П = mgh. Кинетическая энергия шара равна нулю, поскольку равна нулю его начальная скорость. В конце качения скорость шара равна v. При этом угловая скорость шара равна ω = v/R, где R – радиус шара, а его кинетическая энергия равна сумме кинетических энергий поступательного движения Кп = mv2/2 и вращательного движения Кв = Jω2/2 =
= 2/5 ∙ m ∙ R2 ∙ (v/R)2/2 = mv2/5 (J = 2/5 ∙ m ∙ R2 – момент инерции шара относительно оси качения), т. е.
К = Кп + Кв = mv2/2 + mv2/5 = 7mv2/10.
По закону сохранения энергии П = К, или
mgh = 7mv2/10,
gh = 7v2/10,
v = √(10gh/7) ≈ √(14h) = 3,74√h – искомая скорость шара.
Ответ: v = √(10gh/7) ≈ 3,74√h.
С уважением.
В начальный момент времени шар обладает потенциальной энергией П = mgh. Кинетическая энергия шара равна нулю, поскольку равна нулю его начальная скорость. В конце качения скорость шара равна v. При этом угловая скорость шара равна ω = v/R, где R – радиус шара, а его кинетическая энергия равна сумме кинетических энергий поступательного движения Кп = mv2/2 и вращательного движения Кв = Jω2/2 =
= 2/5 ∙ m ∙ R2 ∙ (v/R)2/2 = mv2/5 (J = 2/5 ∙ m ∙ R2 – момент инерции шара относительно оси качения), т. е.
К = Кп + Кв = mv2/2 + mv2/5 = 7mv2/10.
По закону сохранения энергии П = К, или
mgh = 7mv2/10,
gh = 7v2/10,
v = √(10gh/7) ≈ √(14h) = 3,74√h – искомая скорость шара.
Ответ: v = √(10gh/7) ≈ 3,74√h.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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