Forces surrounding Car on a Bridge

In summary, the question asks to calculate the additional reaction forces at supports A and B due to the presence of a 7500N car stalled one-quarter of the way across a bridge with a length of AB. After discussing the concept of moments, it is determined that the moment produced by RB about point A would be (AB)*RB, and the moment produced by the 7500N force would be the rotational acceleration around point A. Further calculations are needed to find the exact values of RA and RB.
  • #1
Oktane
4
0

Homework Statement


An W = 7500 N automobile is stalled one-quarter of the way across a bridge (see Fig. P77). Compute the additional reaction forces at supports A and B due to the presence of the car. Take the length of the bridge to be AB.

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Homework Equations





The Attempt at a Solution


I was told that if you pick one side of the bridge as your rotation point, then either A or B is already a length of 0. But I'm not sure how to proceed from here, any help would be greatly appreciated!
 
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  • #2
Call the reaction at A, RA and at B, RB.

So if you take moments about A, then the moment of RA about A is 0 right?

So what is the moment produced by RB about the point A and what is the moment produced by W about A?
 
  • #3
I didn't know what a moment was so I read the explanation but doesn't that mean that the force around point B would just be a normal force of 7500 because the object is static? But that isn't the right answer.
 
  • #4
Oktane said:
I didn't know what a moment was so I read the explanation but doesn't that mean that the force around point B would just be a normal force of 7500 because the object is static? But that isn't the right answer.

a moment is the turning effect produced by a force which acts perpendicular to a body.

So the moment of RB about A, would be the force multiplied by its perpendicular distance from A.
 
  • #5
Oh ok! That makes sense, however the bridge length is only given to be AB. So that would mean, if A was the rotation point, that A=0 and therefore B=7500AB right?
 
  • #6
Oktane said:
Oh ok! That makes sense, however the bridge length is only given to be AB. So that would mean, if A was the rotation point, that A=0 and therefore B=7500AB right?
No the force is RB and the distance is AB , so the moment produce is (AB)*RB Right?

Can you find the moment produced by the 7500N force?
 
  • #7
rock.freak667 said:
No the force is RB and the distance is AB , so the moment produce is (AB)*RB Right?

Can you find the moment produced by the 7500N force?

Would that be the rotational acceleration around point A?
 
  • #8
Dr Meow said:
Would that be the rotational acceleration around point A?

Taking moments about A.
 

1. What is the centripetal force acting on a car as it crosses a bridge?

The centripetal force is the force that keeps an object moving in a circular path. In the case of a car on a bridge, the centripetal force is provided by the bridge's structure and the car's tires gripping the road surface.

2. How does the angle of the bridge affect the forces acting on a car?

The angle of the bridge can affect the forces acting on a car in a few ways. If the bridge is banked (angled), it can help to provide the necessary centripetal force for the car to maintain its circular motion. However, if the angle is too steep, it can increase the risk of the car slipping or sliding off the bridge.

3. What is the role of friction in the forces surrounding a car on a bridge?

Friction plays a crucial role in the forces surrounding a car on a bridge. Friction between the car's tires and the road surface helps to provide the necessary centripetal force for the car to maintain its circular motion. Additionally, friction between the tires and the bridge's surface helps to keep the car from slipping or sliding off the bridge.

4. How does the weight of the car affect the forces on a car crossing a bridge?

The weight of the car can affect the forces on a car crossing a bridge in a few ways. A heavier car will have a greater inertia, meaning it will require a larger centripetal force to keep it moving in a circular path. Additionally, a heavier car will put more weight on the tires, increasing the friction and helping to keep the car on the bridge.

5. What other factors can impact the forces surrounding a car on a bridge?

Other factors that can impact the forces on a car crossing a bridge include the speed of the car, the condition of the road and bridge surface, and the design and construction of the bridge. Additionally, external forces such as wind or other vehicles on the bridge can also affect the forces on a car. It is important for drivers to be aware of these factors and adjust their driving accordingly to ensure safety while crossing a bridge.

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