Question

ÖÊÁ¿Îªm=0.2 kgµÄСÇò´ÓˮƽµØÃæ´¦ÒÔ20m/sµÄËÙ¶ÈÊúÖ±ÉÏÅ×£¬ÄÜÉÏÉýµÄ×î´ó¸ß¶ÈΪ16m£¬È»ºóÂä»ØˮƽµØÃ棬ÓëˮƽµØÃæ·¢ÉúÅöײºóÔÙ´ÎÉÏÉý£¬ÉÏÉýµÄ¸ß¶ÈΪ7 m¡£¶øºóÓÖÂä»ØˮƽµØÃæ¡­£¬Ö±µ½×îºó¾²Ö¹ÔÚˮƽµØÃæÉÏ£¬ÉèСÇòÊܵ½µÄ¿ÕÆø×èÁ¦´óСºã¶¨£¬gÈ¡10 m/s2£¬Çó£º

£¨1£© СÇòËùÊÜ¿ÕÆø×èÁ¦µÄ´óС

£¨2£© СÇòµÚÒ»´ÎÉÏÉýʱ¼äºÍµÚÒ»´ÎÏÂÂäʱ¼äÖ®±È

£¨3£© ´ÓСÇò¸Õ¿ªÊ¼ÉÏÅ×µ½µÚ¶þ´Î¼´½«Â䵽ˮƽµØÃæÉÏ֮ǰµÄ¹ý³ÌÖÐËðʧµÄ»úеÄÜ

 

Answer 1

£¨1£© СÇòµÚÒ»´ÎÉÏÉý¹ý³ÌÖУ¬Óɶ¯Äܶ¨ÀíµÃ£º - £¨mg + f£©h1 = 0 - mvo2    

´úÈëÊý¾Ý½âµÃ£¨2 + f £©¡Á16 = ¡Á0.2¡Á202    ¡à   f = 0.5N   

£¨2£© СÇòµÚÒ»´ÎÉÏÉý¹ý³ÌÖмÓËٶȴóСΪ

 a1 = £¨mg + f £©/m = £¨2 +0.5£©/0.2 = 12.5 m/s2  

µÃÉÏÉýËùÓÃʱ¼äΪ£º  t1 =        

СÇòµÚÒ»´ÎÏÂÂä¹ý³ÌÖмÓËٶȴóСΪ£º

a2 = £¨mg - f£©/m = £¨2 - 0.5£©/0.2 = 7.5 m/s2   

µÃÏÂÂäËùÓÃʱ¼äΪ£º t2 =   ¡à  ʱ¼äÖ®±ÈΪ£ºt1/t2 =  =    

£¨3£© µÚÒ»´ÎÂä»ØµØÃæʱµÄËٶȴóСΪ v1£¬Ôò 2 f h1 = m£¨vo2 - v12£© 

½âµÃ v1 =  m/s     ÉèµÚ¶þ´ÎÉÏÉýʱ³õËÙ¶ÈΪv2 £¬ 

Ôò £¨mg + f £©h2 =m v22  ½âµÃ v2 = 5 m/s  СÇòÓëµØÃæײ»÷ʱËðʧµÄÄÜÁ¿  

∆E1 = mv12 - mv22 = ¡Á0.2¡Á£¨240 - 175£©= 6.5J       

СÇòÔÚ¿ÕÆøÖÐËðʧµÄ»úеÄÜΪ

∆E2 = f£¨2h1 + 2h2£© = 0.5¡Á£¨2¡Á16 + 2¡Á7£© =  23J        

´ÓСÇò¸Õ¿ªÊ¼ÉÏÅ×µ½µÚ¶þ´ÎÂ䵽ƽÃæ֮ǰµÄ¹ý³ÌÖÐËðʧµÄ»úеÄÜΪ

∆E = ∆E1 +∆E2 = f£¨2h1 + 2h2£©+mv12 -mv22 = 23 + 6.5 = 29.5 J   

Ò²¿ÉÒÔÏÈÇó³öµÚ¶þ´ÎÂä»ØµØÃæʱËٶȵĴóС v3£¬ÔòÓУº£¨mg ¨C f £©h2 =m v32 

¡à  mv32 = £¨0.2¡Á10 - 0.5£©¡Á7 = 10.5

Ôò ∆E= mvo2 ¨Cm v32 = ¡Á0.2¡Á202 - 10.5 = 40 - 10.5 = 29.5 J 

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