Does Resultant Force Directly Influence Direction in Linear Motion?

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In linear motion, a body moves in the direction of the resultant force acting on it, confirming that the acceleration aligns with this force. The discussion highlights that in circular motion, the object moves away from the point of tangency, while in linear motion, the direction of motion corresponds to the resultant force. The vertical forces in a scenario, such as a lawn mower being pushed, indicate that the normal force adjusts to balance the weight and any additional vertical forces applied. Newton's Third Law is referenced to explain how the normal force increases with downward force. Overall, the acceleration of a body is always directed towards the resultant force, influencing its displacement.
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For linear motion.. is it true that a body will point in the direction of the resultant force?

This seems true to me because the I know that in circular motion, the object will fly from the point of tangency when released.
And the point of tangency for linear motion is in the direction of the motion...

Is this correct?

2nd question:
I added a picture of a lawn mower being pushed by force (P) and moving horizontally.
How would the vertical forces zero out, would this mean that the normal force is not equal to the weight force?
 

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The normal force simply increases due to Py--this makes sense by Newton's Third Law. If I push down hard on a table, there's an equal and opposite force (i.e. it "pushes" up) (unless I push so hard that it breaks). So from your equation, we have N = Py + w.

I don't really know what you mean by a body "pointing". Keep in mind though, for circular motion, the acceleration points towards the center of the circle.
 
I meant to say.. the body's displacement is in the direction of the resultant force...

Thus is moves in the direction of Px
 
Is my question still not making sense?
 
The acceleration is always in the direction of the resultant force. When a car brakes to a stop, what is the direction of the acceleration? The resultant force? The displacement?
 
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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