问题 计算题

如图所示,一辆载重卡车沿平直公路行驶.车上载有质量均为m的A、B两

块长方体水泥预制件。已知预制件左端与车厢前挡板的距离为L,A、B间以及B与车厢间的动摩擦因数分别为,各接触面间的最大静摩擦力等于滑动摩擦力。卡车以速度匀速行驶时,因前方出现障碍物而制动并做匀减速直线运动。问:

(1)卡车制动的加速度满足什么关系时,预制件A相对B滑动,而B相对车厢底板静止?

(2)卡车制动后为保证司机安全,在B相对车厢底板静止的情况下,预制件A不与车厢前挡板碰撞,则卡车从开始制动到停止所经历的时间应满足什么条件?

答案

(1)(2) 

题目分析:解:(1)若A相对B滑动,则有:   (2分)

即:  (1分)

若B相对车厢底板滑动,则有:   (2分)

即:   (1分)

要使A相对B滑动,需满足   (1分)

要使B相对于车厢底板静止,需满足  (1分)

联立以上各式得: (1分)

(2)卡车制动后,设A的位移为s1,有 (1分)

卡车的位移为s,有:  (2分)

要使A不与车厢的前挡板相碰,应满足   (1分)

 (1分)

故:   (1分)

设卡车制动时间为t,则有  (2分)

 (1分)

完形填空
完形填空。
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