质量是60 kg的人站在升降机中的体重计上,当升降机做下列各种运动

质量是60 kg的人站在升降机中的体重计上,当升降机做下列各种运动时,体重计的读数是多少?(g=10 m/s2

(1)升降机匀速上升;

(2)升降机以4 m/s2的加速度匀加速上升;

(3)升降机以5 m/s2的加速度匀加速下降。

答案

(1)600N  (2) 840N   (3) 300 N


解析:

人站在升降机中的体重计上受力情况.

(1)当升降机匀速上升时由牛顿第二定律得

F=FN-G=0

所以,人受到的支持力FN=G=mg=60×10N=600N.根据牛顿第三定律,人对体重计的压力即体重计的示数为600N.

(2)当升降机以4 m/s2的加速度加速上升时,根据牛顿第二定律FNG=maFN=Gma=mga)=60×(10+4)N=840N,此时体重计的示数为840N,大于人的重力600 N,人处于超重状态.

(3)当升降机以5 m/s2的加速度加速下降时,根据牛顿第二定律可得mgFN=ma

N=300 N,体重计的示数为300 N,小于人本身的重力,人处于失重状态.

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