Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length script l = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown in the figure below. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero.

http://www.webassign.net/serpse8/12-p-002.gif

Question

Why is the following situation impossible? A uniform beam of mass mb = 3.00 kg and length script l = 1.00 m supports blocks with masses m1 = 5.00 kg and m2 = 15.0 kg at two positions as shown in the figure below. The beam rests on two triangular blocks, with point P a distance d = 0.300 m to the right of the center of gravity of the beam. The position of the object of mass m2 is adjusted along the length of the beam until the normal force on the beam at O is zero. 

http://www.webassign.net/serpse8/12-p-002.gif

anonymous · Answer

Let's sum the torques about P. $$\sum \tau_P = 0 \rightarrow m_b \cdot d - m_2 \cdot x + N_O \cdot {l \over 2} + m_1 \cdot {l \over 2}$$Noting that x is limited to be no greater than 0.2m. 

If this cannot satisfy the equation, such that $N_O=0$, it will be impossible.

anonymous · Answer

Thanks so much!!