Suggestions:
- FBD
- Newton-Euler equations: You can use equations (1) and (2) along with EITHER (3a) OR (3b) above. The advantage of using (3a) over (3b) is that you have one fewer term on the RHS. However, with (3b) you do not need to deal with the reaction forces Px and Py (note that Px and Py create moments about G but not moments about P). Also, point G is the center of mass of the TOTAL system (particle and bar). This is NOT at the midpoint of the bar; rather, you need to use the equation for finding the center of mass of a composite body (as you did in ME 270).
- Kinematics: Since the bar does not rotate, alpha = 0. Also, aGx = aP = a, and aGy = 0.
- Solve: Combine your equations to solve for a.
Let us know if you have any questions on this.
5 comments:
What is the equation for finding the center of mass of a composite body? All the equations I find require an area not just a length and mass.
I actually solved it without finding the center because you know that the relative acceleration is zero, but if you do need to find it i am preetty sure you can just add the centers of the two geometric shapes.
I am confused regarding how to find I_p. I understand that it is the rotational motion of the body about its center, but do not know how to relate that to the equation M_p = I_p *(alpha). Any suggestions?
--to Eric--
There are several forms of the equation for finding the center of mass for a composite body. For a one-dimensional body such as the bar + particle here, you should use the following form:
x_cm = (m_particle*x_particle + m_bar*x_bar)/(m_particle + m_bar)
With m_particle = m_bar in this problem, you will find that the center of mass of the bar + particle is at 3/4 the length of the bar.
--to J.T.--
In this problem, we are looking for the pendulum to have a CONSTANT 15 degree deflection. Therefore, alpha for the pendulum is zero. You do not need to actually find I_P here since it is multiplied by a zero alpha.
[As noted in the Suggestions, M_P is NOT equal to I_P*alpha. You need the full form of Euler's equation if you choose point P.]
In today's class we will talk about how to find I_P for a rigid body.
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