Statics problem, trailer and truck system

[yaro99]

Homework Statement

Homework Equations

ƩF_x=0
ƩF_y=0
ƩM=0

The Attempt at a Solution

I will call the tire forces A (for the trailer), and B and C (for the truck)

I got the correct answer for A by isolating the trailer and writing this equation for it:
ƩM_D = 2400*9 - 2*A*11 = 0
A = 982lb ↑

to find D, I wrote this equation, still just for the trailer:
ƩF_y = 2*A - 2400 + D = 0
2*982 - 2400 + D = 0
D = 436lb ↑

I got the wrong answers for B and C.
To find them, I tried isolating the truck and using these equations:
ƩM_C = 2900*4 - 2*B*9 - D*12 = 0
2900*4 - 436*12 - 18*B = 0
B = 354 lb ↑

ƩF_y = D + 2*B - 2900 +2*C = 0
436 + 2*354 - 2900 + 2*C = 0
C = 878lb ↑


Also, I inadvertently found the answer to part (b) when I started the problem by calculating the equilibrium equations for the truck that I wrote above, but forgetting to factor the truck's weight into the equations. I'm not sure why this would yield the correct answer; I would appreciate it if someone could try to explain that.

 

[haruspex]

D = 436lb ↑

I got the wrong answers for B and C.
To find them, I tried isolating the truck and using these equations:
ƩM_C = 2900*4 - 2*B*9 - D*12 = 0

You found that from the trailer's perspective D acts upwards. Which way does it act from the truck's perspective?

 

[yaro99]

You found that from the trailer's perspective D acts upwards. Which way does it act from the truck's perspective?

Ah, thank you!
It is pointing down from the truck's perspective, so the signs should be switched on the 2 equations. This gives me the right answer.

I am still curious about part b) though. Why is the truck's weight omitted in the calculation?

 

[SteamKing]

Looks to me like the weight of the truck (2900 lbs) is included in the calculations.

 

[haruspex]

I am still curious about part b) though. Why is the truck's weight omitted in the calculation?

Since it is asking for the extra load that results from the trailer, I don't understand why you think the truck's weight should be relevant (as long as it weighs enough to stop the trailer flipping backwards).

Looks to me like the weight of the truck (2900 lbs) is included in the calculations.

I think yaro99 is referring to an earlier (unposted) attempt at part a.

 

[yaro99]

Looks to me like the weight of the truck (2900 lbs) is included in the calculations.

Using these equations yields the correct answer for part b), when I plug in 436 for D:
ƩM_C = -2*B*9 + D*12 = 0
ƩFy = -D + 2*B +2*C = 0

ΔB = +291lb
ΔC = -72.7lb
Weight is not included in the above equations. I'm just not sure why this is the right answer.

 

[SteamKing]

Well, the trailer is pushing down on the hitch. It stands to reason that the truck would see an increase in the load put on the rear wheels while the front wheels would see a reduction in the load. Imagine the truck rotating counterclockwise due to the hitch load.