Question

如圖3－2－16所示，在高出水平地面h＝1.8 m的光滑平臺上放置一質(zhì)量M＝2 kg、由兩種不同材料連接成一體的薄板A，其右段長度l₁＝0.2 m且表面光滑，左段表面粗糙．在A最右端放有可視為質(zhì)點的物塊B，其質(zhì)量m＝1 kg，B與A左段間動摩擦因數(shù)μ＝0.4.開始時二者均靜止，現(xiàn)對A施加F＝20 N水平向右的恒力，待B脫離A(A尚未露出平臺)后，將A取走．B離開平臺后的落地點與平臺右邊緣的水平距離x＝1.2 m．(取g＝10 m/s²)求：

圖3－2－16

(1)B離開平臺時的速度v_B.

(2)B從開始運動到剛脫離A時，B運動的時間t_B和位移x_B.

(3)A左段的長度l₂.

Answer 1

解析　(1)設物塊B平拋運動的時間為t，由運動學知識可得

h＝gt²                                                                                                                                                                                                                                     ①

x＝v_Bt                                                                                                                       ②

聯(lián)立①②式，代入數(shù)據(jù)得

v_B＝2 m/s                                                                                                                 ③

(2)設B的加速度為a_B，由牛頓第二定律和運動學的知識得

μmg＝ma_B                                                                                                                                                                                                                                 ④

v_B＝a_Bt_B                                                                                                                                                                                                                                       ⑤

x_B＝a_Bt_B²                                                                                                                                                                                                                                           ⑥

聯(lián)立③④⑤⑥式，代入數(shù)據(jù)得

t_B＝0.5 s                                                                                                                   ⑦

x_B＝0.5 m                                                                                                                 ⑧

(3)設B剛開始運動時A的速度為v₁，由動能定理得

Fl₁＝Mv₁²                                                                                                                                                                                                                         ⑨

設B運動后A的加速度為a_A，由牛頓第二定律和運動學的知識得

F－μmg＝Ma_A                                                                                                                                                                                                                     ⑩

l₂＋x_B＝v₁t_B＋a_At_B²                                                                                                                                                                                                             ⑪

聯(lián)立⑦⑧⑨⑩⑪式，代入數(shù)據(jù)得

l₂＝1.5 m                                                                                                                  ⑫

答案　(1)2 m/s　(2)0.5 s　0.5 m　(3)1.5 m