Sir Lancelot rides out of the castle at Camelot and onto the 12.0 m long drawbri

Question

Sir Lancelot rides 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 cable (60 degree angle with the horizontal) holding up the front end of the bridge so that it will break under a tension of. The bridge weighs 1900 N and it is uniform. Lancelot, his lance and armor and his horse have a combined weight of 5800 N. Will the cable break before Lancelot reaches the end of the drawbridge? If so, how far from the castle will he be when the cable breaks? (measure from the castle to the center of mass) A force of 2100 N is placed on the sprocket of a motorcycle wheel as show in the diagram. The radius of the sprocket, r, is 5.25 cm while the inner and outer radii of the tire (R_1 and R_2) are 30.0 cm and 36.0 cm respectively. The mass of the tire is 10.5 kg. (a) What is the magnitude and direction of the torque on the tire? (b) What is the angular acceleration of the tire? A solid sphere, a hollow sphere and a solid cylinder all of equal mass and radii are released from rest at a height h and allowed to roll down an inclined plane. If they all roll without slipping calculate the velocities of each at the bottom of the plane as a function of h. Find the equations for and rank the objects from least to greatest angular velocity

Explanation / Answer

Given the length(L) of the bridge is = 12.0m

weight of the bridge is(m) = 1900kg

Maximum tension in the cable is (Tmax) =This value is missing in the problem.

The combined weight of the Lancelot, his lance, his armor andhis horse together is (M) = 5800kg

The center of the bridge is at the center that is at l =6.00m

Now if Lancelot were at the end of the bridge the tension inthe cable is find out as

               TL = MgL + mg(L/2)

   T(12.0m) =(5800N)(12.0m) +(1900N)(6.0m)

                 T =6750N

Compare this value with maximum allowed strength and then see either it can withstand or not.

In order to prevent the breaking of the cable the maximumdistance(x) he has to travel on the bridge is to becalculated.

It is calculated as TL = Mgx + mg(L/2)

Here T = 5800N (it is considered as this value please re do the calculation with the given tension value).

Now (5800N)(12.0m) = (5800)(x) +(1900)(6.0m)

                                

By calculating we get the value of x is (x) = 10.03m

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