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When a bus stops suddenly, I can "feel" a force pushing me. This is exactly as if someone really pushed me. Same is the case while doing a turn in a car, I can "feel" a force pushing me away from the centre. Also, why don't we feel the inward centripetal force but only the outward centrifugal force? If its only because of inertia, then why aren't they considered real forces since inertia is a fundamental property of matter. Everywhere I've read it says that pseudo forces are only incorporated to validate Newton's second law in non - inertial frames. But if they're not actual physical forces, then what is the force that I "feel"? Is there any other cause for pseudo forces other than inertia?

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marked as duplicate by sammy gerbil, Jon Custer, peterh, David Hammen, John Rennie newtonian-mechanics Jun 20 '17 at 5:40

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If you stand in a bus on roller skates (friction free) and the bus suddenly accelerates you will feel nothing.
You will certainly feel the back of the bus pushing on you when you reach the back of the bus.

If there is friction between your feet and the floor of an accelerating bus what you feel is the force of the bus on your feet.
That force which the bus has applied on you not only produces an translational acceleration of your centre of mass it also produces a torque on you which produces a rotational acceleration, you start to topple.
To stop that happening you grab hold of a vertical metal rod attached to the bus which then also applies a force on you and results in there being no net torque acting on you; you have stopped rotating (toppling).

A seated passenger accelerating with the bus watching you accelerate backwards could account for all that what was seen by applying Newton's laws of motion in the bus assuming an extra (pseudo) force was acting on you.

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Imagine you are in a truck which is moving with constant velocity.As far as you are concerned the truck is stationaru with respect to you.If there is a ball lying in the truck it will be stationary too.Imagine the truck brakes(decelerates).The ball will now be thrown towards the front of the truck.If you had no idea that the truck was moving it would appear as if a force had acted on the ball although no force would be visible.Hence the word pseudoforce and it originates due to inertia and it's direction is always opposire to the acceleration. Imagine a ball tied to a string and whirled around.The force it experiences is the tension from the string keeping it from moving outwards.Thats how it continues to move in a circle.The same is what we experience when a car turns...the walls of the wall press us inwards so that circular motion is continued.The tendency due to inertia is to shoot out at a tangent to the circle.If we cut the string of the thread the ball flies of at a tangent due to inertia.Same our tendency should the car move in circle and brake suddenly. This inertial tendency to shoot out at a tangent can be represenfed by a pseudoforce which is opposite to the diection of actual acceleration which is named ascentrifugal force and gives workable results.

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The force that you can "feel" is not somebody pushing you towards the front of the bus, but instead somebody pulling your feet away to the direction of the back. And This is a "real" force. The ground of the sus exerts it onto you, and you exert it in reverse direction onto the ground of the bus.

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