Question

如圖5－1－21所示，質(zhì)量為M的拖拉機(jī)拉著耙來耙地，由靜止開始做勻加速直線運(yùn)動(dòng)，在時(shí)間t內(nèi)前進(jìn)的距離為s.耙地時(shí)，拖拉機(jī)受到的牽引力恒為F，受到地面的阻力為自重的k倍，耙所受阻力恒定，連接桿質(zhì)量不計(jì)且與水平面的夾角θ保持不變．求：

圖5－1－21

(1)拖拉機(jī)的加速度大�。�

(2)拖拉機(jī)對(duì)連接桿的拉力大小．

(3)時(shí)間t內(nèi)拖拉機(jī)對(duì)耙做的功．

Answer 1

解析　(1)由勻變速直線運(yùn)動(dòng)的公式：s＝at²                                                                                                       ①

得：a＝                                                                                                              ②

(2)設(shè)連接桿對(duì)拖拉機(jī)的拉力為f.由牛頓第二定律得：

F－kMg－fcos θ＝Ma                                                                                        ③

根據(jù)牛頓第三定律，聯(lián)立②③式，解得拖拉機(jī)對(duì)連接桿的拉力大小為：f′＝f＝

                                                                                                ④

(3)拖拉機(jī)對(duì)耙做的功：W＝f′xcos θ                                                                 ⑤

聯(lián)立④⑤式，解得：W＝s                                                         ⑥

答案　(1)　(2)

(3)s