Question

如圖7所示，光滑斜槽水平末端與停在光滑水平面上長(zhǎng)為L(zhǎng)="2.0" m的小車上表面在同一水平面上，小車右端固定一個(gè)彈性擋板（即物體與擋板碰撞時(shí)無(wú)機(jī)械能損失）.一個(gè)質(zhì)量為m="1.0" kg的小物塊從斜槽上高h(yuǎn)="1.25" m處由靜止滑下沖上小車，已知小車質(zhì)量M="3.0" kg，物塊與小車間動(dòng)摩擦因數(shù)為μ=0.45，g取10 m/s².求整個(gè)運(yùn)動(dòng)過(guò)程中小車的最大速度.

圖7

Answer 1

1.5 m/s.
評(píng)分標(biāo)準(zhǔn)：①②③式各2分，④⑤⑥⑦式各1分.

物塊滑到小車上時(shí)的初速度為v₀，則mgh=mv²₀，v₀="5" m/s                   ①
設(shè)物塊與擋板相碰，則碰后瞬間小車速度最大，此時(shí)物塊、小車速度分別為v₁、v₂則
mv₀=mv₁+Mv₂                                                                ②
μmgL=mv²₀-mv₁²-Mv₂²                                                 ③
所以2v₂²-5v₂+3=0
所以v₂="1" m/s或v₂="1.5" m/s                                                     ④
討論：①當(dāng)v₂="1" m/s時(shí)，v₁="2" m/s>v₂，此為碰前瞬間的速度                        ⑤
②當(dāng)v₂="1.5" m/s時(shí)，v₁="0.5" m/s<v₂，此為碰后瞬間的速度                           ⑥
即小車的最大速度為1.5 m/s                                                    ⑦