What is the Net Force Acting on an Object on an Inclined Plane?

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To determine the net force acting on an object on an inclined plane, focus on calculating the overall net force without needing to distinguish between specific forces like gravity or friction. The problem provides sufficient information, such as distance, time, and mass, to compute the magnitude of the net force. The direction of the net force is assumed to align with the incline but cannot be definitively calculated due to a lack of information regarding friction or other forces. If the friction coefficient were known or if the plane were assumed to be frictionless, direction could be determined. Ultimately, the question primarily seeks the magnitude of the net force.
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Homework Statement



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The Attempt at a Solution



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I really am lost after that. Any tips? Did I even write the next force equations correctly? :\
 
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Use kinematics.

(Hint: the problem statement doesn't ask you to distinguish between gravitational force, frictional force, or any other particular forces. It's only asking you to find the overall net force. Knowing the distance, the time it takes to accelerate over this distance, and finally the mass of the object are all you need to calculate this net force.)

[Edit: Well, enough information is given for you to calculate the magnitude of of the net force. The net force's direction is assumed to be along the direction of the plane, whatever that happens to be. (Don't bother trying to calculate the direction. Not enough information is given.)]

[2nd edit: You could calculate the direction if you knew what the friction coefficient was, or knew you were suppose to assume the plane is frictionless. But since the problem statement doesn't say anything about friction or lack thereof, or whether or not there are some other forces besides the obvious, there's not enough information to determine the direction. I'm guessing the question is just looking for the magnitude.]
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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