What mistakes may be causing discrepancies in the solution for the force P?

[Krappy]

Homework Statement

The linkage ABD is formed by connecting two 8.05-lb bars and a collar of negligible weight. The motion of the linkage is controlled by the force applied to the collar. Knowing that a tthe instant shown the angular velocity and angular acceleration of bar B are zero and 10 rad/s² counterclockwise, respectively, determine the force P.

http://img685.imageshack.us/img685/5416/picxv.png

Homework Equations

$$\sum \tau = I\alpha$$
$$\sum F = m a_G$$
$$\vec a_G = \vec a_B + \vec a_{G/B}$$

The Attempt at a Solution

Considering the vertical bar (1):
$$a_B = \alpha_1 L$$
$$\tau = LF = I\alpha_1 \Rightarrow F = \frac{I\alpha_1}{L} = \frac{mL\alpha_1}{3}$$

Now, the horizontal one (2):
$$a_{Gx} = a_B = \alpha_1 L$$
$$P\cos \theta - F = ma_{Gx} = m \alpha_1 L \Leftrightarrow P \cos \theta = m\alpha_1 L (1 + 1/3) \Leftrightarrow P = \frac{4m \alpha_1 L}{3\cos \theta}$$


I know this isn't correct (it doesn't match the solutions), but I can't figure out what I'm doing wrong.


Regards

 

[anathema]

,

Scientist

Dear Scientist,

Thank you for your response and attempt at solving the problem. However, there are a few mistakes in your solution that may be causing the discrepancy with the correct solution.

Firstly, in your calculation for the moment of inertia (I), you have not taken into account the fact that the two bars are connected at point B. This means that the moment of inertia should be calculated about the point B, rather than the center of mass of each bar. This will change the value of I and therefore affect your calculations for the force P.

Additionally, in your calculation for the horizontal bar (2), you have used the acceleration of bar 1 (a_B) instead of the acceleration of bar 2 (a_{Gx}). This will also affect the final result for the force P.

I suggest reviewing your calculations and making sure that you are using the correct values for I and a_{Gx}. Also, double check your trigonometric calculations when solving for the force P.

I hope this helps. Good luck with your solution.
Scientist