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Консультация № 176790
20.02.2010, 13:19
42.08 руб.
0
1
1
Здравствуйте, эксперты.
Как решить эту задачу:
Камень брошен под углм 45o к горизонту с начальной скоростью 20 м/с.
1. Чему равны его тангенциальное и нормальное ускорения через 0.5 с. после броска?
2. Чему равны эти составляющие полного ускорения в точке наивысшего подъема?
3. Чему равняются радиусы кривизны траектории в точках 1. и 2.?
Сопротивлением воздуха пренебречь.
Как решить эту задачу:
Камень брошен под углм 45o к горизонту с начальной скоростью 20 м/с.
1. Чему равны его тангенциальное и нормальное ускорения через 0.5 с. после броска?
2. Чему равны эти составляющие полного ускорения в точке наивысшего подъема?
3. Чему равняются радиусы кривизны траектории в точках 1. и 2.?
Сопротивлением воздуха пренебречь.
Обсуждение
20.02.2010, 17:14
общий
это ответ
Здравствуйте, Иванов Андрей Владимирович.
если пренебречь сопротивлением воздуха, то горизонтальная составляющая скорости постоянна
vx=v0*cos[$945$]=20м/с*cos45[$186$]=10[$8730$]2=14,14 м/с
вертикальная составляющая меняется по закону
vy=v0*sin[$945$]-g*t
в точке 1 (при t1=0,5с)вертикальная составляющая скорости
vy1=v0*sin[$945$]-g*t1=9,24 м/с
тангенс угла к горизонту tg[$946$]=vy1/vx=0,654
[$946$]=33,17[$186$]
нормальное ускорение aн1=g*cos[$946$]=0,837g=8,2 м/с2
Тангенциальное ускорение ат1=-g*sin[$946$]=-0,547g=-5,36 м/с2
радиус кривизны
R1=v12/aн1=(vx2+vy12)/aн1=34,8 м
В верхней точке траектории:
направление движения горизонтальное - vy2=0
нормальное ускорение aн2=g=9,8 м/с2
Тангенциальное ускорение ат2=0 (так как ускорение свободного падения перпендикулярно направлению движения)
радиус кривизны траектории R2=v22/aн2=vx2/g=20,4 м
если пренебречь сопротивлением воздуха, то горизонтальная составляющая скорости постоянна
vx=v0*cos[$945$]=20м/с*cos45[$186$]=10[$8730$]2=14,14 м/с
вертикальная составляющая меняется по закону
vy=v0*sin[$945$]-g*t
в точке 1 (при t1=0,5с)вертикальная составляющая скорости
vy1=v0*sin[$945$]-g*t1=9,24 м/с
тангенс угла к горизонту tg[$946$]=vy1/vx=0,654
[$946$]=33,17[$186$]
нормальное ускорение aн1=g*cos[$946$]=0,837g=8,2 м/с2
Тангенциальное ускорение ат1=-g*sin[$946$]=-0,547g=-5,36 м/с2
радиус кривизны
R1=v12/aн1=(vx2+vy12)/aн1=34,8 м
В верхней точке траектории:
направление движения горизонтальное - vy2=0
нормальное ускорение aн2=g=9,8 м/с2
Тангенциальное ускорение ат2=0 (так как ускорение свободного падения перпендикулярно направлению движения)
радиус кривизны траектории R2=v22/aн2=vx2/g=20,4 м
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