[請益] 機械力學的問題
請問各位大大幫我看看我是否有答錯,這是97年鐵路原級的試題
一電扇已1200rpm之速度迴轉,今突然斷電,使葉片之轉速在5sec內變為600rpm,
請問葉片在5sec內共轉幾轉?而使葉片完全停止還須多少時間?
A.解答上的計算方式:
1.
w1=1200/(60*2π)=3.18 rad/s
5秒後速度w2=600/(60*2π)=1.59 rad/s
w2=w1+at
角加速度a=(1.59-3.18)/5=-0.318 rad/s^2
w2^2=w1^2+2aθ
5秒內轉的角度θ=11.94 rad
葉片在五秒共轉11.94/2π=1.9轉
2.
0=1.59+(-0.318)t
T=5sec
B.我的計算方式
1.
w=2πn/60
w2=(2π*1200)/60=40π
w1=(2π*600)/60=20π
w2=w1+at
20π=40π+5a
a=-4π rad/s^2
θ=w1t+0.5at^2
θ=40π*5+0.5*(-4π)*25=150π
葉片在五秒共轉150π/2π=75轉
2.
0=20π+(-4π)t
T=5sec
請問各位大大我的觀念哪裡有錯誤嗎?
跟解答的答案有很大的落差
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