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Friction on Bounce?

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I have this system with gravity parallel to y-coordinate and floor parallel to x-coordinate. A particle (represented by a sphere) held a distane above the floor. suddenly the particle is thrown into the air and moves into projectile due to gravity. As soon as it hits the floor, it bounces off. Upon collision response an assuming there is no friction between particle and floor, the velocity of the particle gets reflected back upwards (away from the floor). Since the floor is parallel to x-axis, only the y-component of the particle is changed. Now what if there's friction between particle and floor? understand that if say the particle is already in constant contact with the floor, but moving in parallel to the floor (sliding), it will slow down and stop at some point due to friction. now my problem is, how do i calculate the actual effect of friction when the particle is still bouncing? specifically at the point when the particle hits the floor at instant and bounces off?

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What you get is a non-normal bounce, i.e. your bounce is not necessarily perpendicular to the surface.

The direction of the bounce, i.e. of the force and impuse that makes it up, will tend to be in the opposite direction to the direction of impact. E.g. a particle travelling at 45 degrees to the surface when it hits it will experience an impuse at 45 degrees to the surface.

BUT this is limited by friction: the coeffcient of friction (COF) limits the ratio of the horizontal force to the vertical force. This means the total force (horizontal + vertical) cannot be more than angle theta from the normal, where tan theta = COF. No friction, i.e. COF = 0, and the force is of course perpendicular.

The effect of this force is generally not to throw the object back in the direction it came from as the impuse will change both the velocity and rotation speed of the particle. For a sphere this only happens with friction as it's only a rough contact that generates a torque. So the object bounces off and spins, and the ratio of change in angular velocity/change in angular momentum depends on the moment of inertia.

If the particle is already spinning it can hit a surface at right angles and bounce off at an angle, as the friction of it's moving surface colliding with the surface push it off sideways. I.e. the most general case involves a rotating object hitting a surface at any angle.

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but what if the the object is non-rigid body?, a particle that doesn't rotate? and has only linear velocity? once it hits the floor when moving in projectile, what's the effect of friction between the particle and floor?

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Quote:
Original post by Aquarian
but what if the the object is non-rigid body?, a particle that doesn't rotate? and has only linear velocity? once it hits the floor when moving in projectile, what's the effect of friction between the particle and floor?


If the particle doesn't rotate, then the force of friction either doesn't matter, because there is no sliding involved between the particle and the floor, or the force of friction is calculated based on the delta-v between the horizontal motions of the floor and the particle and imparts angular momentum on the particle.

The real issue here is the modulus involved between the projectile and the floor, I suspect, in how much pressure is applied between them. Where there is no force between the two object (perfectly inelastic collision), no change in angular momentum will occur. Where the particle goes "splat" with a relatively elastic collision, it starts rolling instead of bouncing, like a koosh ball.

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so does it means that as long as the object(non-rigid body) is bouncing (not sliding yet) against the floor(it's static), i can just ignore the friction force parrallel to the floor and not consider into the collision response?

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Quote:
Original post by Aquarian
but what if the the object is non-rigid body?, a particle that doesn't rotate? and has only linear velocity? once it hits the floor when moving in projectile, what's the effect of friction between the particle and floor?


Then you're not dealing with real physics. A body with mass also has volume and size otherwise it would have infinite density. If it has volume and mass it has a non-zero moment of inertia and so in general an impulse applied to it produces both linear and rotational effects.

You don't need to follow all the ruls of physics - few games do. So you could supress rotational effects by e.g. setting the moment of inertia to infinity (things then don't rotate as it would take an infinite amount of energy or infinite force to get them to rotate).

What you'll then get is, as long as the angle of impact (measured from the normal) is less than tan-1 COF, particles will be sent back the way they came as the force/impulse acts in that direction as long as they are in contact with the surface and none of its effect is "lost" rotating particles. If the angle with the normal is too big the friction will not be enough to return them the way it back the way they came and they will be reflected somewhere between this direction and a frictionless reflection).

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