Finding Maximum Force for Sled Without Lifting

[yitriana]

Homework Statement

A dog pulls a sled with unspecified force at 25° above horizontal. Mass of sled-passenger-rope partile is 80 kg and there is negligible friction. Find the maximum magnitude of force F that can be applied to the rope without lifting the sled off the surface.

Homework Equations

sum of forces = ma
normal force is F_n
mass of particle is m

The Attempt at a Solution

F_xnet = Fcos(25) = ma_x
F_ynet = Fsin(25) - 9.8*m + F_n

In any case where the sled is not lifted, F_ynet = 0, since acceleration is in direction of x only (for this problem).

However, I am confused about how to find maximum force before sled is lifted.

 

[method_man]

When you start to lift the sled you have: Fsin(25)= 9.8*m. In that moment, you have no F_n because the sled is not touching the ground.

 

[RoyalCat]

Don't think of being lifted off the ground in terms of the net force, but in terms of the normal. When the normal is 0 or negative, then you have lift-off.

Though the two approaches are completely equivalent, I find that, personally, the latter is simpler to follow.