作业帮大学物理问题（英文写的.但是很好理解）
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大学物理问题（英文写的.但是很好理解）
Three identical books of length L are stacked over the edge of a table as shown in Figure Q6.The top book overhangs the middle one by L/2,so it just barely avoids falling.The middle book overhangs the bottom one by L/4.How much of the bottom book can be allowed to overhang the edge of the table without the books falling?
A box is put on a scale that is marked in units of mass and adjusted to read zero when the box is empty.A stream of marbles is then poured into the box from a height h above its bottom at a rate of R (number of marbles per second).Each marble has mass 𝒎𝟎.If the collisions between the marbles and the box are completely inelastic,find the scale reading at time t after the marbles begin to fill the box.
Three identical books of length L are stacked over the edge of a table as shown in Figure Q6.The top book overhangs the middle one by L/2,so it just barely avoids falling.The middle book overhangs the bottom one by L/4.How much of the bottom book can be allowed to overhang the edge of the table without the books falling?
A box is put on a scale that is marked in units of mass and adjusted to read zero when the box is empty.A stream of marbles is then poured into the box from a height h above its bottom at a rate of R (number of marbles per second).Each marble has mass 𝒎𝟎.If the collisions between the marbles and the box are completely inelastic,find the scale reading at time t after the marbles begin to fill the box.
1)假设底书出桌边x,三本书均重G,有：
对于桌边,上书力矩（重量*重心＝重量*（书边-半长））：T1=G×(x+L/2+L/4-L/2)
对于桌边,中书力矩：T2=G×(x+L/4-L/2)
对于桌边,下书力矩：T3=G×(x-L/2)
依据平衡关系:T1+T2+T3=0
解得：x=L/6
2)离地h高的石头掉地时需要的时间为T=√(2h/g)
从而在t时时刻：
当t
对于桌边,上书力矩（重量*重心＝重量*（书边-半长））：T1=G×(x+L/2+L/4-L/2)
对于桌边,中书力矩：T2=G×(x+L/4-L/2)
对于桌边,下书力矩：T3=G×(x-L/2)
依据平衡关系:T1+T2+T3=0
解得：x=L/6
2)离地h高的石头掉地时需要的时间为T=√(2h/g)
从而在t时时刻：
当t