Question #177180

The final answer should be in the format of "tolerance of ± in the third significant digit."


1.The slotted arm OA forces the small pin to move in the fixed spiral guide defined by r =  where θ is measured in radians and the constant K = 3.9 m. Arm OA starts from rest at θ = 31° and has a constant counterclockwise angular acceleration θ¨= 2.2 rad/s2. Determine the magnitude a of the acceleration of the pin P when θ = 148°.


a = _ m/s2

1
Expert's answer
2021-04-05T11:12:34-0400

ar=r¨rθ˙2=K(θ¨θθ˙2)=3.9(2.237π45θ˙2),a_r=\ddot r-r\dot{\theta }^2=K(\ddot{\theta}-\theta \dot{\theta}^2)=3.9\cdot(2.2-\frac{37\pi}{45}\cdot \dot{\theta}^2),

aθ=rθ¨+2r˙θ˙=K(θθ¨+2θ˙2)=3.9(37π452.2+2θ˙2),a_{\theta}=r\ddot{\theta}+2\dot{r}\dot{\theta}=K(\theta \ddot{\theta}+2\dot{\theta}^2)=3.9\cdot(\frac{37\pi}{45}\cdot 2.2+2\dot{\theta}^2),

a=ar2+aθ2=3.9(2.237π45θ˙2)2+(37π452.2+2θ˙2)2.a=\sqrt{a_r^2+a_{\theta}^2}=3.9\cdot\sqrt{(2.2-\frac{37\pi}{45}\cdot \dot{\theta}^2)^2+(\frac{37\pi}{45}\cdot 2.2+2\dot{\theta}^2)^2}.


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