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Консультация № 160023
09.02.2009, 17:13
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Здравствуйте, помогите решить задачу. Определить КПД неупругого удара бойка массой т1 = 0,5 т, падающего на сваю массой т2 = 120 кг. Полезной считать энергию, затраченную на вбивание сваи. Заранее спасибо )
Обсуждение
Неизвестный
09.02.2009, 21:50
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это ответ
Здравствуйте, Попов Антон Андреевич!
____________________
Определить
КПД неупругого удара бойка массой
m1 = 0,5 т,
падающего на сваю массой
m2 = 120 кг.
Полезной считать энергию, затраченную на вбивание сваи.
________________
Импульсы до удара и после равны
p1+p2= p
Импульс и энергия бойка перед ударом
p1= m1*v1
E1= m1*v1^2/2
Импульс и энергия сваи перед ударом
p2= 0
E2= 0
Импуль и энергия системы "свая+боек" после удара, энергия системы "свая+боек" тратится на работу по преодолению силы сопротивления грунта. То есть по условию задачи это полезная работа.
p= p1+p2= m1*v1= (m1+m2)*v
E= (m1+m2)*v^2/2
v= v1*m1/(m1+m2)
E= (m1+m2)*v1^2*m1^2/(2*(m1+m2)^2)= v1^2*m1^2/(2*(m1+m2))= E1*(m1/(m1+m2))
КПД= E/E1= m1/(m1+m2)
КПД= 500/(500+120)= 0,806= 80.6%
____________________
Определить
КПД неупругого удара бойка массой
m1 = 0,5 т,
падающего на сваю массой
m2 = 120 кг.
Полезной считать энергию, затраченную на вбивание сваи.
________________
Импульсы до удара и после равны
p1+p2= p
Импульс и энергия бойка перед ударом
p1= m1*v1
E1= m1*v1^2/2
Импульс и энергия сваи перед ударом
p2= 0
E2= 0
Импуль и энергия системы "свая+боек" после удара, энергия системы "свая+боек" тратится на работу по преодолению силы сопротивления грунта. То есть по условию задачи это полезная работа.
p= p1+p2= m1*v1= (m1+m2)*v
E= (m1+m2)*v^2/2
v= v1*m1/(m1+m2)
E= (m1+m2)*v1^2*m1^2/(2*(m1+m2)^2)= v1^2*m1^2/(2*(m1+m2))= E1*(m1/(m1+m2))
КПД= E/E1= m1/(m1+m2)
КПД= 500/(500+120)= 0,806= 80.6%
Форма ответа
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