Why does friction point the opposite as gravity?

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Friction always acts against the direction of motion, not necessarily against gravitational force. In the case of the piano on the incline, friction opposes the component of gravity pulling it down the slope, aiding the man in preventing acceleration. The force exerted by the man is calculated by subtracting the friction force from the gravitational component along the incline. Understanding that friction acts on the relative motion of surfaces clarifies its direction; it helps prevent sliding rather than opposing gravity directly. Thus, friction's role is to resist any tendency for surfaces to move relative to each other.
Shindo
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Homework Statement


a 280-kg piano slides 4.3m down a 30 degree incline and is kept from accelerating by a man who is pushing back on it parallel to the incline.

I know how to find the solution, but there's something that I don't understand about why it's that way. In order to find the force the man needs to exert to keep it from accelerating you subtract the friction force by the component of gravity. But I don't get why you subtract it rather than adding it. If it is not accelerating how do you determine which direction the friction force is acting? At first I thought it would be along the same direction of the horizontal component of gravity because it slides down that way, but instead friction is helping the man in this case. Why does it point against gravity and how are you able to tell? Thanks!
 
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Friction always acts against motion. Acceleration is irrelevant here.
For example, if you throw a ball up in the air, its acceleration will always be the same - g pointing down, but the direction of velocity will change from up to down, and similarly the air resistance (friction) will change direction as well.
 
Bandersnatch said:
Friction always acts against motion.
To be precise, it acts against relative motion of surfaces in contact. Thus, friction does not act to oppose the motion of a rolling ball on a level surface, since even if friction were to suddenly vanish the surfaces in contact would not move relative to each other. Similarly, friction does not oppose the forward movement of a driven car. It opposes the tendency for the wheels to skid, so it acts forwards, propelling the car.
 
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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