Answer to Question #177180 in Classical Mechanics for Joseph Se

Question

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 = Kθ 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

Answer 1

$a_r=\ddot r-r\dot{\theta }^2=K(\ddot{\theta}-\theta \dot{\theta}^2)=3.9\cdot(2.2-\frac{37\pi}{45}\cdot \dot{\theta}^2),$

$a_{\theta}=r\ddot{\theta}+2\dot{r}\dot{\theta}=K(\theta \ddot{\theta}+2\dot{\theta}^2)=3.9\cdot(\frac{37\pi}{45}\cdot 2.2+2\dot{\theta}^2),$

$a=\sqrt{a_r^2+a_{\theta}^2}=3.9\cdot\sqrt{(2.2-\frac{37\pi}{45}\cdot \dot{\theta}^2)^2+(\frac{37\pi}{45}\cdot 2.2+2\dot{\theta}^2)^2}.$