Question

The slotted arm revolves in the horizontal plane about the fixed vertical axis through point O. The 2.2-lb slider C is drawn toward O at the constant rate of 3.6 in./sec by pulling the cord S. At the instant for which r = 7.5 in., the arm has a counterclockwise angular velocity ω = 6.3 rad/sec and is slowing down at the rate of 2.1 rad/sec 2. For this instant, determine the tension T in the cord and the force N exerted on the slider by the sides of the smooth radial slot. The force N is positive if side A contacts the slider, negative if side B contacts the slider.

Answer 1

T = 2.5 lb

N= -0.33 lb

Step-by-step explanation:

given

r = 9 in

`\dot{r} =-3.6 in/s and\ \ddot{r} = 0`

`\dot{\theta} = 6.3\ rad/s and\ \ddot{\theta} = 2.1\ rad/s^2`

`-T = m a_r = m(\ddot{r} -r{\dot{\theta}^2)`

`N= m a_(\theta) = m(r\ddot{\theta}+2\dot{r}\dot{\theta}})`

`T= mr{\dot{\theta}^2 = (3)/(386.4)(9)(6)^2 =2.5lb`

`N= m(r\ddot{\theta}+2\dot{r}\dot{\theta}})=(3)/(386.4)[9(-2)+2(-2)(6)]=-0.326 lb`