一道英文的物理题,急(关于energy)A simple pendulum of length 2.00 m is made with a mass of 2.00 kg.The mass has a speed of 3.00 m/s when the pendulum is 30.0o above its lowest position.What is the maximum angle away from the lowest posit

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一道英文的物理题,急(关于energy)A simple pendulum of length 2.00 m is made with a mass of 2.00 kg.The mass has a speed of 3.00 m/s when the pendulum is 30.0o above its lowest position.What is the maximum angle away from the lowest posit
一道英文的物理题,急(关于energy)
A simple pendulum of length 2.00 m is made with a mass of 2.00 kg.The mass has a speed of 3.00 m/s when the pendulum is 30.0o above its lowest position.What is the maximum angle away from the lowest position the pendulum will reach?

一道英文的物理题,急(关于energy)A simple pendulum of length 2.00 m is made with a mass of 2.00 kg.The mass has a speed of 3.00 m/s when the pendulum is 30.0o above its lowest position.What is the maximum angle away from the lowest posit

1/2mv^2=mgh
1/2*2*3^2=2*10*h
h=0.45m
(Lcos30-h)/L=cosA
cosA=(2*1.732/2-0.45)/2=0.641
A=carcos0.641=50度

从本题题意来看,要分两种情况讨论。

以钟摆最低点为基准参考点,设该点时钟摆速度为v

      ①情况1时,小球达到最高点时

          1/2mv^2+mg(1-sin60°)L=mgh1

        h1=?(不好意思,手头没有计算器。)

        角度α1=arccos[(L-h1)/L]

      ②情况2时,因为不考虑空气阻力,此为理想钟摆模型,故当其摆至右侧对称位置时,与情况1类似(图形为现在情况1沿轴对称到右侧)

         所以计算情况与①相同,α2=arccos[(L-h1)/L]

所以综上所述,夹角为----度。

不好意思,数值自己代入下吧。科学计算器上都有相应按键算。

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According to law of conservation of mechanical energy, the follwoing equation can be wretten:
1/2*m*v^2+mgL(1-cos30°)=mgL(1-cosθ) (1)
1/2*m*9+mg*2*(1-cos30°)=mg*2*(1-cosθ)
so the maximum angle θ is
θ=arccos0.416=65.42°