why does a ball roll down a hill
If you increase the steepness of the ramp, then you will increase the
acceleration of a ball which rolls down the ramp. This can be seen in two different ways: 1) Components of forces. Forces are vectors and have a direction and a magnitude. The force of gravity points straight down, but a ball rolling down a ramp doesn't go straight down, it follows the ramp. Therefore, only the component of the gravitational force which points along the direction of the ball's motion can accelerate the ball. The other component pushes the ball into the ramp, and the ramp pushes back, so there is no acceleration of the ball into the ramp. If the ramp is horizontal, then the ball does not accelerate, as gravity pushes the ball into the ramp and not along the surface of the ramp.
If the ramp is vertical, the ball just drops with acceleration due to gravity. These arguments are changed a bit by the fact that the ball is rolling and not sliding, but that only affects the magnitude of the acceleration but not the fact that it increases with ramp steepness. 2) Work and energy. The change in potential energy of the ball is its mass times the change in height (only the vertical component counts -- horizontal displacements do not change gravitational potential energy) times the local gravitational acceleration g. This loss of gravitational potential energy shows up as an increase in kinetic energy. If the ball falls a farther distance vertically, it will have a greater kinetic energy and be going faster. Again, the kinetic energy is shared between the motion of the ball going somewhere, and the rotation of the ball, and so the details of the acceleration depend on the ball (is it hollow or solid? ), but the dependence on the steepness of the ramp is the same. (published on 10/22/2007) Sometimes injuries happen quickly.
They are the result of an accident or a fall, and the pain is obvious and immediate. But many are more subtle. I like to explain it to my patients with the analogy of rolling a ball down a hill. If a ball is sitting at the top of a hill, all you need to do is give it a small push and gravity does the rest. At first it doesnБt look like much. If the hill isnБt too steep you may not see much movement. It may get held up by some tall grass or get stuck in a small hole.
But just one or two tiny pushes and it starts again, gathering speed and before you know it, that ball is out of your control and flying down the hill. Most back injuries start off the same way. Slowly, hardly moving at all but gathering momentum until they are out of control and the pain is severe. It is only when the pain gets out of control that most patients even notice that there is a problem. Then they come to with injuries that have been developing for a long time. We can almost always help with their pain, but depending on the how long the condition has existed and how Бfar down the hillБ they have gone, sometimes we canБt push that ball all the way to the top of the hill again. For some people the best we can do is to stop the rolling and keep them from going further down the hill.
But thereБs more to it than that. Once we have helped with the pain, the ball is still sitting on a hill, but weБve stopped it from rolling further down the hill by putting our foot on the ball. If we take our foot off, the ball slowly begins to roll down the hill again and before you know it, the pain is back and getting worse faster than ever. That is why we continue to see and even after they have gotten out of pain, and why we give them exercises to increase their strength. Because if we just ignore they problem, then weБre letting that ball start rolling down that hill again, and itБs only a matter of time before the problem is worse than ever.
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