Calculating Forces and Equilibrium of a Drawbridge

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In summary, the drawbridge in the given figure has its weight supported entirely by its hinges and the opposite shore, with slack cables. The fraction of weight supported by the opposite shore when the point of support is under the cable attachments is 1/6. The direction and magnitude of the force exerted by the hinges on the bridge is determined by solving the simultaneous equations for the vertical and horizontal components of the forces, with the additional condition that the total horizontal force on the bridge is zero. This allows for the determination of the value of F and θ, with Fsinθ=20416 being the given equation. The direction of F must be chosen carefully to satisfy the condition that the total horizontal force on the bridge is zero.
  • #1
hndalama
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Homework Statement


Suppose the weight of the drawbridge in Figure is supported entirely by its hinges and the opposite shore, so that its cables are slack. (a) What fraction of the weight is supported by the opposite shore if the point of support is directly beneath the cable attachments? (b) What is the direction and magnitude of the force the hinges exert on the bridge under these circumstances? The mass of the bridge is 2500 kg.
Here's a link to the figure
https://cnx.org/resources/8186f1166e382ac9ec92644a6613ce07451f29c1/Figure_10_03_10a.jpg
Figure_10_03_10a.jpg


2. Homework Equations
I use net fore = 0 and net torque=0
T=0 because it is slack, N = normal force
Fsinθ + N = w
1.5Fsinθ = 7.5N

The Attempt at a Solution


I find N by solving the simultaneous equation to get Fsinθ= 20416 and N=4083 so the fraction for a is 1/6
I am stuck on question b. I know Fsinθ=20416 but I don't know how to find the value of F and θ.
 
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  • #2
The condition "net force = 0" is actually two conditions. One condition for the vertical components of the forces and the other condition for the horizontal components of the forces.
 
  • #3
TSny said:
The condition "net force = 0" is actually two conditions. One condition for the vertical components of the forces and the other condition for the horizontal components of the forces.
so I have to include the equation Fcosθ - Nx=0
Nx = Normal force in the x direction, since depending on the value of Fcosθ, the bridge will press against the wall

Now I have 3 variables and only two equations (i.e Fsinθ=20416). How do I solve for F and θ?
 
  • #4
You can assume that the right end of the drawbridge just sits on the ledge without pressing on the wall. So, the normal force is vertical.
 
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  • #5
It might help to note that the picture is drawn for the general case where there is tension in the cable. For the special case where there is no tension in the cable, the force F might not be in the direction as shown in the picture. You will need to decide what the direction of F must be in order to satisfy the condition that the total horizontal force on the bridge is zero.
 
  • #6
thank you
 

FAQ: Calculating Forces and Equilibrium of a Drawbridge

1. What is drawbridge equilibrium?

Drawbridge equilibrium is a principle in game theory that describes a situation where two players have equal power and are both equally motivated to make a move. This creates a state of balance where neither player can gain an advantage without risking their own position.

2. How is drawbridge equilibrium different from other equilibrium concepts?

Drawbridge equilibrium differs from other equilibrium concepts in that it focuses on the balance of power between two players, rather than the balance of payoffs. In other equilibrium concepts, players are more concerned with maximizing their own gains, whereas in drawbridge equilibrium, players are more focused on maintaining their position.

3. What factors influence drawbridge equilibrium?

There are several factors that can influence drawbridge equilibrium, including the players' abilities, their level of trust in each other, and the potential consequences of making a move. These factors can shift the balance of power and ultimately affect the equilibrium state.

4. How is drawbridge equilibrium used in real-world situations?

Drawbridge equilibrium can be applied to a variety of real-world situations, such as negotiations, conflict resolution, and business partnerships. It can help parties find a mutually beneficial solution and avoid escalating conflicts.

5. Can drawbridge equilibrium be broken?

Yes, drawbridge equilibrium can be broken if one player gains a significant advantage or if the balance of power shifts in favor of one player. This can happen if one player makes a strategic move or if external factors, such as market changes, influence the situation.

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