Question

如圖，質(zhì)量為m=1kg的木樁豎直插在沙中，質(zhì)量為M=4kg的鐵錘從木樁的正上方離木樁上端H=5m高處自由落下，鐵錘擊中木樁后不反彈，在極短時(shí)間內(nèi)兩者達(dá)到共同速度一起豎直向下運(yùn)動，經(jīng)時(shí)間t=0.1s停下．（不計(jì)空氣阻力和碰撞時(shí)間，g取10m/s²）求：                                                                                                          

①鐵錘和木樁的共同速度大小；                                                                                 

②木樁受到沙的平均作用力大�。�                                                                              

                                                                                                                   

                                                                                                                                  

Answer 1

解：①鐵錘下落過程，機(jī)械能守恒，由機(jī)械能守恒定律：

，

打入數(shù)據(jù)得：v₁=10m/s，m/s，

鐵錘與木樁相撞過程動量守恒，以鐵錘的初速度方向?yàn)檎�方向，由動量守恒定律得�?/p>

Mv₁=（M+m）v₂，

代入數(shù)據(jù)得：v₂=8m/s；

②鐵錘和木樁一起向下運(yùn)動，由動量定理：

（F﹣Mg﹣mg）t=（M+m）v₂，

代入數(shù)據(jù)得：F=450N；

答：①鐵錘和木樁的共同速度大小為8m/s；

②木樁受到沙的平均作用力大小為450N．