Question

有一个边长为的正方形桌子，桌面离地高度为。一个质量为的小物块可从桌面中心点以初速沿着桌面任意方向运动直至落地。设动摩擦因素为 （取），求

（1）设物块在桌面滑动距离为，求物块刚离开桌面时的速度与的关系。

（2）物块在桌面滑动距离为多大时，物块水平运动距离最大？最大距离为多少？

（3）物块水平运动距离最大时，物块运动的总时间为多少？

 

Answer 1

【答案】

（1）        根据动能定理可得：

                                                                                                                                                               1

可求出：

                                                                                                                                                                             2

（2）        离开桌子后，物块做平抛运动

 

                                                                                                                                                                                                       

                                                                                                                                                                                                 

得 

                                                                                                                                                           3

代入已知条件

                                                                                                                                                                                       

令，得到：

                                                                                                                                                                               4

当 ，即时，总的水平运动距离取得极大值

                                                                                  。                                                                           5

（3）        由

                                                                                            

可得物块在桌面运动时间为

                                                                                                                                                                                             6

从而得， 且可知平抛运动时间为

所以总运动时间为

      

【解析】略