**1. The problem statement, all variables and given/known data**

In the picture below, we see a scene from the days of yore. This is called a tow path and the situation is that a barge is being towed by some horses along the side of a canal. Let’s say the horses pull with 6200 N of force at an angle of θ=16∘. If the barge has a mass of 2528 kg, and magnitude of its acceleration is 1.47 m/s2, find the magnitude of the force on the barge from the water.

Here’s a picture of the angle between the rope and the barge. Assuming I’m reading it correctly, it’s with respect to the vertical component (so the barge isn’t too far behind the horses)

**2. Relevant equations**

F sin θ = Fx

F cos θ = Fy

F = ma

**3. The attempt at a solution**

Just to start off, I want to say that I figured out the answer, but I’m not sure why the answer is what it is.

I tried to calculate the horizontal component of the force applied by the horses (which would be 6,200 * sin 16, or 1,709.95 N). Then, the total force on the barge would be 3,716.16 N (due to F = ma). So the force on the barge should be the difference between the total force and the force applied by the horses, which was 2,006.21 N.

I sent this explanation to my professor, and he said that the acceleration is only happening in the y-direction. But that doesn’t make sense, because the horses are dragging the barge in the x-direction. He said Fnet x would be 6200sin16 – Fwater x = 0 (which makes sense if there’s no acceleration on the x-axis). Then he told me to figure out the equation for Fnet y, which would be 6200cos16 – Fwater y = 3,716.16 N (because F=ma).

So then I solved for Fwater x and Fwater y, and used the Pythagorean theorem to calculate that the net force of the water was 2820.40 N, which was the correct answer.

So ultimately, my question is: Why is the barge accelerating vertically instead of horizontally? It’s not like the horses are pulling it out of the water. Unless the buoyant force is normally cancelled out by the gravitational force, but the upward force exerted by the horses is causing upward acceleration. But then why is there no horizontal acceleration?

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