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Thecla
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Is it possible to make the coefficient of friction between a ball and an inclined plane low enough so that a ball will silde down the plane and not roll down the plane?
Thecla said:Is it possible to make the coefficient of friction between a ball and an inclined plane low enough so that a ball will silde down the plane and not roll down the plane?
If you roll a ball down an inclined plane, the accelerating force (parallel to the inclined plane) is proportional to mg sin(θ), while the force pushing the ball against the inclined plane is mg cos(θ). If the ball has a moment of inertia (e.g., I = 2mR2/5 for a solid ball), a decelerating force parallel to the inclined plane (and opposite to mg sin(θ)) is required just to spin the ball. If the angle of the inclined plane exceeds a critical angle, the force pushing the ball against the inclined plane is insufficient to make the ball spin, even if the coefficient of friction is 1.kgbgru said:Unless it is zero there will be a force between the ball and surface that will cause the ball to spin. That dosen't mean it won't slide, however any friction will make it spin.
The sloped belt would have to be continously accelerating "uphill" in order to keep the ball in a stationary position. The belt speed and the ball's angular velocity would be constantly increasing.tadietz said:How would you diagram/describe all of the forces involved in a system where a solid sphere is rolling down a sloped belt (like a conveyor belt, say) that is moving up (i.e., the top surface of the belt where the sphere contacts it is moving toward the top of the slope), and given this construction, could there ever be an equilibrium reached where the forces imparted by the friction between the two objects (belt and sphere) and all the other forces involved (gravity, rotational inertia, etc.) cause the ball to remain stationary (but still rotating, of course) relative to a stationary observer?
rcgldr said:The sloped belt would have to be continously accelerating "uphill" in order to keep the ball in a stationary position. The belt speed and the ball's angular velocity would be constantly increasing.
Ball sliding and rolling are two different types of motion that a ball can exhibit. Sliding occurs when the ball is in contact with a surface and moves due to a force acting on it. Rolling, on the other hand, is when the ball rotates on its axis while moving forward. In rolling, the ball maintains contact with the surface at all times.
The speed of a ball sliding or rolling can be affected by several factors, including the surface it is moving on, the force applied, the shape and size of the ball, and any external forces acting on it, such as friction or air resistance.
Yes, a ball can exhibit both sliding and rolling motion at the same time. This can happen when the ball is on a surface with low friction, such as ice, and has enough force applied to make it slide and roll simultaneously.
The weight of a ball does not directly affect its sliding or rolling motion. However, a heavier ball may require more force to start sliding or rolling and may also be more resistant to changes in motion due to its inertia.
A common real-life example of ball sliding and rolling is a bowling ball. The ball slides as it moves down the lane before transitioning to a rolling motion towards the pins. Another example is a soccer ball, which slides when kicked and then rolls on the ground. Other examples include marbles rolling down a ramp and a billiard ball sliding and rolling on a pool table.