Equilibrium Question on Bridge

1. Oct 23, 2005

erik-the-red

Question

Sir Lancelot rides slowly out of the castle at Camelot and onto the 12.0-m-long drawbridge that passes over the moat. Unbeknownst to him, his enemies have partially severed the vertical cable holding up the front end of the bridge so that it will break under a tension of $$5.80 \times 10^{3}\;{\rm N}.$$ The bridge has mass 200 kg and its center of gravity is at its center. Lancelot, his lance, his armor, and his horse together have a combined mass of 600 kg.

1. Will the cable break before Lancelot reaches the end of the drawbridge?

Yes. 600 + 200 = 800 (kg). 800 * 9.80 = 7840 N > 5800 N.

2. How far from the castle end of the bridge will the center of gravity of the horse plus rider be when the cable breaks?

I'm thinking $$\sum \tau = (600)(x) - (200)(6.00) = 0$$.

x=2 m.

Is this correct?

2. Oct 23, 2005

Pyrrhus

At what angle is the Tension directed? Is there a picture you can post?

3. Oct 23, 2005

erik-the-red

Sure. I don't think there should be an angle involved; I may be wrong.

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4. Oct 23, 2005

erik-the-red

My answer was wrong because I did not figure in the tension and I did consider units.

$$\sum \tau = (600)(9.80)(x) + (200)(9.80)(6) = (5.38*10^3)(12)$$
$$x=9.84$$ m.

5. Oct 23, 2005

Pyrrhus

The picture is not clear for me, i only see the reaction force by the articulation support and the weight of the bridge and of the knight.