高三机动车辆启动过程的几种图象分析

高三机动车辆启动过程的几种图象分析 机动车辆启动过程的几种图象分析 动车辆的启动方式大致有两种:一种是以恒定功率启动，另一种是以恒定加速度启动。因为机动车启动过程问题涉及到受力分析、牛顿运动定律、运动学、动能定理以及功率计算等方面的知识点，也是联系实际、解决实际生活、工农业生产的典型问题。更重要的是大多数试题往往结合相关图象进行考查。这类题目文字叙述给出的已知条件较少，往往要求从图象中获取相关信息 一、过程分析:以水平面上机动车的启动为例，假设机车在启动过程中所受的地面摩擦阻力和空气阻力恒定不变，在分析的过程中涉及的公式有:;;在匀加速运动阶段、;在达到额定功率以后。以上各式中:示机车发动机功率，即机车发动机牵引力的功率，为机车启动的加速度，表示机车牵引力，并不表示机车受到的合外力，表示以额定功率运动过程的牵引力做功。所以可以得出，机车的启动过程有以下两种方式: 1(以恒定加速度启动:汽车先做初速为零的匀加速直线运动，当发动机功率达到额定值时做加速度逐渐减小的变加速直线运动，直到加速度减小到零时开始做匀速直线运动。 2(以恒定功率启动:先做加速度逐渐减小的变加速直线运动，直到加速度减小到零时开始做匀速直线运动。 二、实例分析: 机动车的启动过程涉及到的图象有:图象、图象(为发动机的牵引力)、图象(为发动机功率)、图象、图象等。 1(和图象:这两类图象反应了机动车在启动过程中速度和发动机功率随时间的变化情况，是最常见的、较易分析的图象类型。 【例1】汽车在平直的公路上由静止启动，图象甲表示汽车运动的速度与时间的关系，图象乙表示汽车牵引力的功率与时间的关系。设汽车在运动过程中阻力不变，在18s末汽车的速度恰好达到最大。求: (1)汽车受到的阻力和最大牵引力; (2)汽车在做变加速运动过程中的位移。 【分析】(1)从图象可以看出，汽车在 做初速度为零的匀加速运动，在 做加速度减小的变加速运动，后做匀速运 动。汽车做匀加速运动的最大速度，而最 Chapter I General provisions article I obligation to clear credit pre-loan investigation requirements, improve the quality of pre-loan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial bank credit small business due diligence guidelines (trial) and other regulatory requirements and the actual situation of the Bank, these measures are formulated. Second person mentioned in these measures refers to in accordance with the rules of credit investigations, surveys and analysis of the credit business people. Article credit mentioned in these measures refers to table provided to customers both inside and outside of the Bank's credit business, including foreign currency loans, trade finance, bank acceptances, commercial bill discounting, guarantees, factoring, credit, loan commitment, guarantee and other credit operations, excluding client credit business. Prior to the chengdai investigation into the fourth article this refers to credit before the review, investigators by obtaining, verification, analysis and security aspects of the situation, evaluation and reveals the possible credit risks and to propose preventive measures. Article fifth due diligence in these measures refers to the person in the pre-loan investigation procedures fulfilling the most basic due diligence requirements. Article sixth of themselves, pre-loan investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal. Chapter II due diligence due diligence work is the basic requirement of the seventh article: follow the principles of true, complete, valid, and diligence due diligence in carrying out investigation duties. Investigators should be based on the characteristics of different varieties of credit business, credit 终做匀速运动的速度，从图象可以看出，汽车的额定功率 。由得汽车受到的阻力: 由题意分析可知，汽车在匀加速运动过程中受到的牵引力最大，当匀加速运动过程的速度为时功率恰好达到，所以最大牵引力: (2)由图线甲可得汽车做匀加速运动的加速度:;对匀加速运动过程由牛顿第二定律得:。解得汽车的质量 对汽车在内做变加速运动，设其变加速直线运动的时间为，则，由动能定理得:。解得: 【点拨】这类题目文字叙述较简单，全部需要通过图象获取信息，包括机车启动过程的详细的运动特点以及各个阶段涉及的数据。所以，只有对每个阶段的运动特点以及每两种运动形式的过度点的特征深刻理解、熟练掌握，才能正确应对这些图象问题。 2(图象和图象:这两类图象反映了机车在启动过程中发动机功率和机车速度之间的函数关系。因为，随着机车速度的不断增加，、、三个物理量随之发生变化。下面就机车以恒定加速度启动为例来说明它们之间变化的特点。 ?图甲是图象，图象以、作为纵横坐标，直接反应了与之间的关系，段图象表示机车做匀加速直线运动，牵引力为恒力，随着速度的增加，机车功率逐渐增加，到达点时机车功率达到额定值，段图象表示机车牵引力功率不变，随着速度的增加，机车牵 in the prepossible credit risks and to propose preventive measures. Article fifth due diligence in these measures refers to the person s the e the review, investigators by obtaining, verification, analysis and security aspects of the situation, evaluation and revealns, excluding client credit business. Prior to the chengdai investigation into the fourth article this refers to credit beforratiobank acceptances, commercial bill discounting, guarantees, factoring, credit, loan commitment, guarantee and other credit ope provided to customers both inside and outside of the Bank's credit business, including foreign currency loans, trade finance,able it investigations, surveys and analysis of the credit business people. Article credit mentioned in these measures refers to tBank, these measures are formulated. Second person mentioned in these measures refers to in accordance with the rules of cred ank credit small business due diligence guidelines (trial) and other regulatory requirements and the actual situation of theloan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial b-of preloan investigation requirements, improve the quality -Chapter I General provisions article I obligation to clear credit pre2cs of different varieties of credit business, credit, valid, and diligence due diligence in carrying out investigation duties. Investigators should be based on the characteristimpletehapter II due diligence due diligence work is the basic requirement of the seventh article: follow the principles of true, con investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal. Cloa-loan investigation procedures fulfilling the most basic due diligence requirements. Article sixth of themselves, pre- 引力逐渐减小，机车做变加速直线运动，图象为双曲线的一支。图象的纵横轴与图象包围的面积表示机车牵引力功率。 由于图象的段为双曲线的一支，图象不规则，所以衍生出图乙和图丙两种图象，通过变换坐标轴对应的物理量，使得图象变为直线。 ?图乙是图象，由于图象的横轴为，所以分析图象时应该沿着横轴从右向左分析。图象的段表示随着速度的增加，牵引力恒定不变，此过程为匀加速直线运动。图象的段表示随着速度的增加，牵引力逐渐减小，机车发动机功率不变，此过程为变加速直线运动，点时机车速度达到最大，机车开始匀速直线运动。段图象的斜率表示机车发动机功率。 ?图丙是图象，图象的段表示匀加速直线运动，段表示变加速直线运动。 【例2】在检测某种汽车性能的实验中，质量为?的汽车由静止开始沿平直公路行驶，达到的最大速度为40m/s，利用传感器测得此过程中不同时刻该汽车的牵引力F与对应的速度v，并描绘出F—图象(图象ABC为汽车由静止到最大速度的全过程图象，AB、BO均为直线)。假设该汽车行驶中所受的阻力恒定，根据图线ABC，求: (1)该汽车的额定功率; (2)该汽车由静止开始运动，经过35秒速度达到最大速度 40m/s，求该汽车在BC段的位移。 【分析】(1)由图线分析可知:图线AB表示汽车所受牵引力F 不变，阻力f不变，汽车由静止开始做匀加速直线运动;图线BC的斜率 表示汽车的功率P不变，达到额定功率后，汽车所受牵引力逐渐减小做加速度减小的变加速直线运动，直至达最大速度40m/s;此后汽车做匀速直线运动。由图可知:当最大速度 时，牵引力为 由平衡条件可得: 由公式得:额定功率 匀加速直线运动的末速度求得: (2)汽车由A到B做匀加速直线运动的加速度 设汽车由A到B所用时间为，B到C的时间为，位移为则: it, loan commitment, guarantee and other credit operations, excluding client credit business. Prior to the chengdai investiga, credsiness, including foreign currency loans, trade finance, bank acceptances, commercial bill discounting, guarantees, factoringicle credit mentioned in these measures refers to table provided to customers both inside and outside of the Bank's credit buArt measures refers to in accordance with the rules of credit investigations, surveys and analysis of the credit business people. regulatory requirements and the actual situation of the Bank, these measures are formulated. Second person mentioned in these ank credit small business due diligence guidelines (trial) and otherloan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial b-loan investigation requirements, improve the quality of pre-reChapter I General provisions article I obligation to clear credit p3ties. Investigators should be based on the characteristics of different varieties of credit business, creditseventh article: follow the principles of true, complete, valid, and diligence due diligence in carrying out investigation du. Chapter II due diligence due diligence work is the basic requirement of the loan investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal-gence requirements. Article sixth of themselves, preloan investigation procedures fulfilling the most basic due dili-th due diligence in these measures refers to the person in the prety aspects of the situation, evaluation and reveals the possible credit risks and to propose preventive measures. Article fifsecurition into the fourth article this refers to credit before the review, investigators by obtaining, verification, analysis and 所以可得: B点之后，对车由动能定理可得: 可得: 【点拨】这类图象的两部分虽然都为直线，但横坐标表示速度的倒数，从图象中获取信息难度加大，很难根据图象得出机车启动的运动特点，从而增加了这类题目的难度。这类图象应沿着坐标横轴从右向左的方向，即随着机车速度的不断增大，分析各个阶段的运动特点以及相关物理量的数据。 【例3】如图甲所示，某同学用轻绳通过定滑轮提升一重物，应用传感器(未在图中画出)测得此过程中不同时刻被提升重物的速度与对轻绳的拉力，并描绘出图象。假设某次实验所得的图象如图乙所示，其中时间段内的图象为线段AB，且线段AB与轴平行， 2时间段内的图象为线段BC，，C点以后重物做匀速直线运动。g=10m/s，绳重及一切摩擦和阻力均可忽略不计。 (1)求时间段内物体上升的加速度和时 间段内的细绳拉力功率; (2)求被提升重物在第一个时间段内和第二个 时间段内通过的总路程。 【分析】(1)设时间段内细绳拉力为，C 点细绳拉力为，由题意可知，重物到达C点以后做匀速直线运动，所以 由图象可知，时间段内重物所受拉力保持不变，所以在时间段内重物做匀加速直线运动，且，设其大小为，则根据牛顿第二定律有: 联立解得: 由图象可知，时间段内图象的斜率不变,所以细绳拉力的功率保持不变: hapter II due diligence due diligence work is the basic requirement of the seventh article: follow the principles of true, con investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal. Cloa-loan investigation procedures fulfilling the most basic due diligence requirements. Article sixth of themselves, pre-in the prepossible credit risks and to propose preventive measures. Article fifth due diligence in these measures refers to the person s the e the review, investigators by obtaining, verification, analysis and security aspects of the situation, evaluation and revealns, excluding client credit business. Prior to the chengdai investigation into the fourth article this refers to credit beforratiobank acceptances, commercial bill discounting, guarantees, factoring, credit, loan commitment, guarantee and other credit ope provided to customers both inside and outside of the Bank's credit business, including foreign currency loans, trade finance,able it investigations, surveys and analysis of the credit business people. Article credit mentioned in these measures refers to tBank, these measures are formulated. Second person mentioned in these measures refers to in accordance with the rules of cred ank credit small business due diligence guidelines (trial) and other regulatory requirements and the actual situation of theloan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial b-of preloan investigation requirements, improve the quality -Chapter I General provisions article I obligation to clear credit pre4cs of different varieties of credit business, credit, valid, and diligence due diligence in carrying out investigation duties. Investigators should be based on the characteristimplete (2)设第一段时间为，重物在这段时间内的位移为，则 ，， 设重物在这段时间内的位移为，根据动能定理有: 解得 所以被提升重物在第一时间段内和第二时间段内通过的总路程 【点拨】这个题目的实质为竖直方向上的机车启动，受力情况有所变化，处理方法不变。有些题目还会涉及到斜面上的机车启动问题。 3(图象:这类图象反映了机车发动机功率随机车速度变化的情况，图象直观简单，易于学生理解和读取信息。图象的段表示随着速度的增加，机 车牵引力功率随之增加，机车牵引力不变，机车做匀加速直线运动， 段图象的斜率表示机车牵引力大小。图象的段表示机车功率 不变的变加速直线运动过程。 三:解题策略 1(解决机车启动问题时，首先应该分清是哪种启动方式，然后再分段处理或整体研究。在匀加速直线运动阶段常用牛顿运动定律和运动学公式结合分析，在非匀变速直线运动阶段一般采用动能定理，对于整个运动过程也可采用动能定理运算。 2(除了要搞清各个阶段各个物理量的变化情况之外，还必须要搞清两个运动阶段之间过渡点的特征。可以采用下面的方法帮助学生加深理解:通过过程分析得出图象以后，在 图象上取五个点、、、、，比较这五个点的发动机功率、加速度、牵引力的大小变化情况。可以得出: (1),,,,,; (2),,,,,0; (3),,,, seventh article: follow the principles of true, complete, valid, and diligence due diligence in carrying out investigation du. Chapter II due diligence due diligence work is the basic requirement of the loan investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal-gence requirements. Article sixth of themselves, preloan investigation procedures fulfilling the most basic due dili-th due diligence in these measures refers to the person in the prety aspects of the situation, evaluation and reveals the possible credit risks and to propose preventive measures. Article fifsecurition into the fourth article this refers to credit before the review, investigators by obtaining, verification, analysis and it, loan commitment, guarantee and other credit operations, excluding client credit business. Prior to the chengdai investiga, credsiness, including foreign currency loans, trade finance, bank acceptances, commercial bill discounting, guarantees, factoringicle credit mentioned in these measures refers to table provided to customers both inside and outside of the Bank's credit buArt measures refers to in accordance with the rules of credit investigations, surveys and analysis of the credit business people. regulatory requirements and the actual situation of the Bank, these measures are formulated. Second person mentioned in these ank credit small business due diligence guidelines (trial) and otherloan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial b-loan investigation requirements, improve the quality of pre-reChapter I General provisions article I obligation to clear credit p5ties. Investigators should be based on the characteristics of different varieties of credit business, credit 3(在解决这些涉及图象的机车启动问题时，从图象中获取有用信息是解决问题的重点和突破口，也是解决这类问题的难点所在。一般情况下，除了读取图象中一些特殊点的数据外，还要根据图象分析机车各个阶段的运动特点，同时注意图象的斜率、图象和坐标轴包围面积的物理意义。 总之，不管是在水平面上、斜面上，还是在竖直方向，机车的启动过程仍然是牛顿运动定律、运动学公式以及动能定理的综合应用问题，仍然需要通过受力分析确定机车的运动状态，对不同的运动形式采用不同的公式、定理进行运算，才能以不变应万变，正确处理好这类问题。 loa-loan investigation procedures fulfilling the most basic due diligence requirements. Article sixth of themselves, pre-in the prepossible credit risks and to propose preventive measures. Article fifth due diligence in these measures refers to the person s the e the review, investigators by obtaining, verification, analysis and security aspects of the situation, evaluation and revealns, excluding client credit business. Prior to the chengdai investigation into the fourth article this refers to credit beforratiobank acceptances, commercial bill discounting, guarantees, factoring, credit, loan commitment, guarantee and other credit ope provided to customers both inside and outside of the Bank's credit business, including foreign currency loans, trade finance,able it investigations, surveys and analysis of the credit business people. Article credit mentioned in these measures refers to tBank, these measures are formulated. Second person mentioned in these measures refers to in accordance with the rules of cred ank credit small business due diligence guidelines (trial) and other regulatory requirements and the actual situation of theloan investigation, prevent credit risks, according to the CBRC commercial bank credit due diligence guidelines, commercial b-of preloan investigation requirements, improve the quality -Chapter I General provisions article I obligation to clear credit pre6cs of different varieties of credit business, credit, valid, and diligence due diligence in carrying out investigation duties. Investigators should be based on the characteristimpletehapter II due diligence due diligence work is the basic requirement of the seventh article: follow the principles of true, con investigators relatives or other interested person to apply for the credit business, one should apply for the withdrawal. C