Sled being pulled by two people. Minimum tension and acceleration.

[charlygarcia]

Homework Statement

A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.603, and the kinetic friction coefficient is μk = 0.395. The combined mass of the sled and its load is m = 291 kg. The ropes are separated by an angle φ = 23°, and they make an angle θ = 31.1° with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving?

If this rope tension is maintained after the sled starts moving, what is the sled\'s acceleration?

Homework Equations

F = ma

The Attempt at a Solution

I tried to draw a free body diagram and add the tensions and then substract the friction. I divided 23° by 2, but I'm not sure if that's correct. To get the minimun tension required to get the sled moving I used μs.
I got this equation at the end but I guess it's wrong because I still can't get the right answer for the minimum tension:
2T cos 31.1+ 2T cos 11.5 = μs ( mg - 2T cos 31.1)

 

[mishek]

Hello, check the photo I attached. Does it help?

 

[haruspex]

mishek's diagram helps (calculate T' first). T' will have a vertical component, which will reduce the normal force from the ground, and hence reduce the friction. But T' will also have a moment about the centre of mass, so the sled's weight footprint will not be evenly distributed. I guess you'll have to ignore that awkwardness. (But not the reduced friction.)