Newton s Laws of Motion

Transcription

1 Newton s Laws of Motion So far we have explored kinematics How to quantify motion: position, velocity, and acceleration The use of vectors to analyze three-dimensional motion Now we will address dynamics: the causes of motion Sir Isaac Newton developed in 1687 a powerful set of rules that describe almost all the motion we experience But, it turns out, not motion on very small distance scales (e.g., atoms) or very high speeds (e.g., near the speed of light) The regions of discrepancy are difficult to study experimentally, and the technology to do so wasn t available until ~100 years ago For the remainder of this semester, we ll pretend it s 1850 or so, and assume Newton s Laws are true!

2 Newton s First Law We begin by considering the simplest case of motion: an object at rest If nothing about the object s environment changes, it will remain at rest On the other hand, if something comes along and pushes it, the object will start moving We call any push or pull on a object a force Forces have both magnitudes and directions i.e., they are described by vectors! Now imagine that the force, having started the object in motion, is now removed, and that the object has no other interaction with its environment. What will happen?

3 The correct answer to this question was found by Gallileo Question is harder than it seems because everyday experience points to the wrong answer We observe that after pushing an object to get it moving, it will eventually slow down and stop But that s because other forces (frictional ones, in this case) are acting to slow it down We can reduce these forces (using smoother surfaces, lubricants, etc.) and observe that the object takes longer to stop. Further, consider looking at the object from a different reference frame, moving at constant velocity with respect to the original one In the new frame, (still) no forces act on the object, but it moves at constant velocity Gallileo realized that the logical extrapolation of these ideas was:

4 Consider an object on which no net force acts. If the object is at rest, it will remain at rest. If it is moving with constant velocity, it will continue to do so. When Newton wrote down his rules for dynamics, he adapted this at his First Law Note that the Law refers to the net force. This refers to the vector sum of all the forces acting on an object.

5 Inertial Reference Frames There are some reference frames in which it appears that Newton s First Law is violated For example, imagine you re driving with an object on the passenger seat, and you take a sharp left turn The object may start to move toward the passenger-side window, even though there seems to be no force pushing it in the direction To avoid this confusion, we specify an inertial reference frame as one in which Newton s First Law applies Does this make the First Law circular? No! One we identify a single inertial frame, any other coordinate system moving with constant velocity with respect to it is also an inertial frame Also, once we find an inertial frame, we can be sure that Newton s 2 nd and 3 rd Laws also apply in that frame

6 The ideal intertial frame is one which is not being acted on at all by the environment A spacecraft in deep space, infinitely far from any other object (and with its engines off!) provides the prime example of such a frame Clearly we won t be in such a frame for the demos/labs we do this semester So, we ll treat the Earth s surface as an inertial frame Note that this is an approximation, but like all good approximations: The difference between the approximation and reality is small for the types of motion we ll typically consider It lets us analyze situations much more simply than we could otherwise!

7 The Earth as a Non-Inertial Frame For motion over long distances, the non-inertial nature of the Earth s surface becomes apparent Imagine two objects, starting on the equator One remains there, and the other is launched exactly northward Six hours later, the first object has moved east by about 6000mi, due to the Earth s rotation The second object has also moved 6000mi east But for points not on the equator, 6000mi is more than ¼ around the Earth The moving object appears to drift eastward due to the Coriolis Force But it s not a force at all just the consequence of a noninertial frame!

8 The Coriolis effect is usually too small to notice, but can have big impact: