Question 42

[McatCrusher]

Hi,
Is the word "uniform bar" the key to knowing that the length of the bar is one meter?

Thank you

[admin]

Not exactly. Uniform refers to the fact that the bar is even throughout. In other words it's not shaped like, for example, a baseball bat which tapers at one end. The importance for the MCAT is that a uniform bar has the center of mass exactly 1/2 the distance to either end.

The length of the bar was never given. We can only discuss the fraction of length x. To simplify, one can assume the length is 1 to simplify calculations but with the understanding that the answer is really just a fraction because we can't know the absolute value.

[mcat_premed3832]

Hmmm, that's very odd! All the "+" symbols are missing from your copy and paste! Did you review your answers using Firefox?

Anyways, I have put in the + signs below. Please note that mg cancels.

Note that the lever arm of the bar is 1/4 because the center of gravity of the bar is at its midpoint and the fulcrum is 3/4 of the length of the uniform bar. Summing these equations together :

Σ L = Σ Fy + Σ Fx = 0 (where Σ Fx = 0 in this case)

[(2m)g x 1/4] + [(mg) x r] + [-(1/2m)g x 1/4] = 0

2/4 mg + mgr - 1/8 mg = 0 --> 4/8 mg - 1/8 mg = -mgr --> 3/8 mg = - mgr --> r = -3/8

Therefore, the person must be 3/8 x from the bar for the system to be in equilibrium.

[admin]

Bump.