How Much Force Do Pillars Exert with a Parked Car on a Bridge?

[chamonix]

Homework Statement

A uniform bridge 20 m long and weighing 4.00x10^5N is supported by two pillars located 3 m from each end. If a 1.96x10^4 N car is parked 8 m from one end of the brige, how much force does each pillar exert?

Homework Equations

(Fgb*L/2+Fgp*d)/L(sin theta).

The Attempt at a Solution

4x10^5*10+1.96x10^4*8/20(sin 90)=207840
That's what I got as an answer. I don't know if this is correct though. Any help is appreciated. Thank you.

 

[hage567]

No you don't have all of your distances right. The car is 8 m from one end, but how far is it from the pivot point you've chosen (one of the pillars)? Also, the distance of the normal force of the pillar to the pivot point is not 20 m. Draw a diagram and label everything carefully.

Repeat for the other pillar, the answer will be different.

 

[m2003]

I would like to provide some feedback on your solution to the rotational bridge question. It seems like you have correctly used the equation for calculating the force on each pillar, which takes into account the weight of the bridge and the weight of the car. However, I would suggest using the cosine function instead of the sine function, as the angle between the bridge and the horizontal is 90 degrees and not the sine of 90 degrees. Additionally, it may be helpful to label your variables and show your units in your calculation to ensure accuracy. Overall, your approach seems sound, but I would recommend double checking your work and units to ensure the correct answer.