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Консультация № 86687
13.05.2007, 12:00
0.00 руб.
0
1
1
уважаемые эксперты проверьте правильность решения задачи
условия:
1.10. Точка движется по окружности радиусом R = 30см с постоянным угловым ускорением e. Определить тангенциальное ускорение ат точки, если известно, что за время t = 4с она совершила три оборота и в конце третьего оборота ее нормальное ускорение аn = 2.7м/с2
решение:
S = Vo*t + (a*t^2)/2 = (V - a*t)*t + (a*t^2)/2 = V*t - (a * t^2) + (a*t^2)/2 = V*t - (a*t^2)/2
V = sqrt( An*r )
S = 3*2*3.14*R
получилось что a(тенгенс) = - 0,2565
условия:
1.10. Точка движется по окружности радиусом R = 30см с постоянным угловым ускорением e. Определить тангенциальное ускорение ат точки, если известно, что за время t = 4с она совершила три оборота и в конце третьего оборота ее нормальное ускорение аn = 2.7м/с2
решение:
S = Vo*t + (a*t^2)/2 = (V - a*t)*t + (a*t^2)/2 = V*t - (a * t^2) + (a*t^2)/2 = V*t - (a*t^2)/2
V = sqrt( An*r )
S = 3*2*3.14*R
получилось что a(тенгенс) = - 0,2565
Обсуждение
Неизвестный
17.05.2007, 21:10
общий
это ответ
Здравствуйте, OKYHb!
Во-первых, лучше пользоваться не линейной скоростью, а угловой. Во-вторых, какое-то странно решение.
6π = A = ω<sub>0</sub>∙t + e∙t<sup>2</sup>/2
(ω<sub>0</sub>+et)<sup>2</sup>∙R = a<sub>n</sub>
{ 4ω<sub>0</sub> + 8e = 6π
{ ω<sub>0</sub> + 4e = √[a<sub>n</sub>/R] = 3
Для удобства записи я опустил размерность. Подразумеваю СИ.
Из системы получаем:
{ ω<sub>0</sub> = 3(π–1) ≈ 6,425 с<sup>–1</sup>
{ e = ¾(2–π) ≈ –0,856 с<sup>–2</sup>
a<sub>τ</sub> = e∙R ≈ –0,26 м/с<sup>2</sup>
Т.е. решили вы правильно, только точность в 4 знака избыточна, т.к. условия заданы с точностью в 1-2 знака. К тому же, у меня получилось –0,256858 м/с<sup>2</sup>. По этой формуле, наверное, и у вас столько же получится ;-)
Во-первых, лучше пользоваться не линейной скоростью, а угловой. Во-вторых, какое-то странно решение.
6π = A = ω<sub>0</sub>∙t + e∙t<sup>2</sup>/2
(ω<sub>0</sub>+et)<sup>2</sup>∙R = a<sub>n</sub>
{ 4ω<sub>0</sub> + 8e = 6π
{ ω<sub>0</sub> + 4e = √[a<sub>n</sub>/R] = 3
Для удобства записи я опустил размерность. Подразумеваю СИ.
Из системы получаем:
{ ω<sub>0</sub> = 3(π–1) ≈ 6,425 с<sup>–1</sup>
{ e = ¾(2–π) ≈ –0,856 с<sup>–2</sup>
a<sub>τ</sub> = e∙R ≈ –0,26 м/с<sup>2</sup>
Т.е. решили вы правильно, только точность в 4 знака избыточна, т.к. условия заданы с точностью в 1-2 знака. К тому же, у меня получилось –0,256858 м/с<sup>2</sup>. По этой формуле, наверное, и у вас столько же получится ;-)
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