Sir Lancelot Equilibrium Bridge Problem

[Dillio]

Homework Statement

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 * 10^3 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.

Homework Equations

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?

The Attempt at a Solution

I hate to say this, but I have no idea where to start. I tried to solve for the distance by:

Torques = (600)(9.8)(x) - (200)(9.8)(6) = (5.8 * 10^3)(12)

It says my tension value is wrong for what is holding the bridge up. The tension is located 12m from the opening of the castle, but apparently I need to solve for my tension in another way.

Any suggestions?

 

[Doc Al]

I tried to solve for the distance by:

Torques = (600)(9.8)(x) - (200)(9.8)(6) = (5.88 * 10^3)(12)

Why the negative sign between the first two terms? (Those torques are in the same direction--they should have the same sign.) Correct that error and you should be fine.

 

[thomate1]

As a scientist, my response to this problem would be to approach it using principles of mechanics and physics. First, let's consider the forces acting on the bridge and its components. The main forces at play here are the weight of the bridge (200 kg) and the combined weight of Sir Lancelot, his horse, and his equipment (600 kg). These forces act downwards due to gravity.

Next, we need to consider the tension in the cable holding up the front end of the bridge. This tension is exerted in an upwards direction, as the cable is trying to hold up the weight of the bridge and its components. We are given that the cable will break under a tension of 5.80 * 10^3 N, so we can use this information to solve for the distance from the castle end of the bridge where the cable will break.

To do this, we can use the principle of equilibrium, which states that the sum of all forces acting on an object must be equal to zero in order for it to be in a state of equilibrium. In this case, we can set up an equation with the forces acting on the bridge and its components:

ΣF = 0

Where ΣF is the sum of all forces acting on the bridge and its components. We can break this down into two components: the horizontal forces and the vertical forces.

For the horizontal forces, we can see that there are no external forces acting on the bridge in this direction, so the sum of these forces will be equal to zero:

ΣFx = 0

For the vertical forces, we have the weight of the bridge and its components acting downwards, and the tension in the cable acting upwards. So we can set up the following equation:

ΣFy = T - (200 kg + 600 kg) * 9.8 m/s^2 = 0

Where T is the tension in the cable. Solving for T, we get:

T = (200 kg + 600 kg) * 9.8 m/s^2 = 7,840 N

Since we know that the cable will break under a tension of 5.80 * 10^3 N, we can set up another equation to solve for the distance from the castle end of the bridge where the cable will break:

T = (200 kg + 600 kg) * 9.8 m/s^2 = 5.80 *