Finding Maximum Force for Sled Without Lifting

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To find the maximum force a dog can exert on a sled without lifting it, the sled's mass is 80 kg, and the pulling angle is 25° above horizontal. The net force in the vertical direction (Fynet) equals zero when the sled is not lifted, leading to the equation Fsin(25) = 9.8*m. When the sled begins to lift, the normal force (Fn) becomes zero, indicating lift-off. The discussion highlights two approaches to solving the problem, with one being preferred for its simplicity. Understanding the relationship between the applied force and the normal force is crucial for determining the maximum pulling force.
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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 Fn
mass of particle is m

The Attempt at a Solution



Fxnet = Fcos(25) = max
Fynet = Fsin(25) - 9.8*m + Fn

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