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Chapter 1: Q44 P (page 360)

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 served the vertical cable holding up the front end of the bridge so that it will break under a tension of 5.80脳103N. 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. Will the cable break before Lancelot reaches the end of the drawbridge? If so, how far from the castle end of the bridge will the center of gravity of the horse plus rider be when the cable breaks?

Short Answer

Expert verified

The cable will break before Lancelot reaches the end. It will break at 9.84 m from the castle end of the bridge.

Step by step solution

01

The given data

Mass of bridge m1=200kg

Mass of Lancelot m2=600kg

Length of drawbridge L = 12 m

The maximum tension cable can hold Tmax=5.80脳103N

02

Formula used

Torque 蟿=F脳L

Where F is force exerted and L is distance.

03

Check if the bridge will collapse

Let T be the tension in the bridge.

TL=m1gL+m2gL2T(12m)=(600kg)9.80m/s2(12m)+(200kg)9.80m/s2(6m)T=6860N

The tension in wire to cross the bridge is 6860 N which exceeds the maximum tension cable can have, hence cable will break.

04

Find the distance from the castle at which the cable will break

Let x be the distance from the castle at which the cable breaks.

TmaxL=m1gx+m2gL25.8脳103N(12m)=(600kg)9.80m/s2(x)+(200kg)9.80m/s2(6m)x=9.84m

The cable will break at 9.84 m from the castle end of the bridge.

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