Newton s Laws of motion

Transcription

1 Newton s Laws of motion Isaac Newton adapted the research of Galileo Galilei s and others and stated three laws of motion. The first two laws are very different from the third, as we discuss below. Newton s First Law of motion Galileo discovered that an object will continue to move as it had in the past unless an unbalanced force acts on it (for example, an unmoving object remains unmoving, or an object moving at 4.25 m/s west continues to move at 4.25 m/s west unless something a force causes its motion to change). So, the First Law tells us how to recognize a force through its action. If the motion of an object changes, it must have been acted on by a force. Examples of changes in motion include the motion of a thrown football from the time it is in the quarterback s hands until it is caught by the receiver, the motion of a baseball from the time it is picked up by the pitcher until after it has hit the ground and come to rest or been caught and come to rest, or the motion of a roller coaster car. Newton s Second Law of motion Newton recognized that the changes in the positions of objects and their velocities could be found if the object s acceleration were known. The acceleration is a measure of the change in the motion of the object seen when investigating Newton s First Law. That acceleration is the only knowledge required to determine the object s motion (provided we know at a specific time where it was and how fast it was going). The Second Law recognizes that the more inertia (measured by mass) an object has, the harder it is for a

2 2 given net force to change the motion. As discussed in the chapter text, the net force required to give an object of mass 2m the same acceleration as the mass m is twice as great as the net force on the first object, the net force required to give an object on mass 3m the same acceleration as m is three times as great, and so on; in other words, acceleration = net force/mass. This law is most often written in the form a, (E3.4.1a) or F = ma. (E3.4.1b) Let s give some examples of the use of Newton s Second Law of motion. An object of mass 3.50 kg is changing its velocity in a specific direction by 2.00 m/s for every second. What net force is being exerted on it that causes this change? According to what we know from Extension 3.2 Average acceleration, the acceleration is the change in velocity divided by the time required to change the velocity; here, that is a = 2.00 m/s 1 s = 2.00 m/s 2, in the direction in which the velocity changes. Now, Newton s Second Law of motion (Eq. E3.4.1a) says that the net force F required is the product of the mass and acceleration, a = (3.50 kg) x (2.00 m/s 2, in the direction in which the velocity changes) = 7.00 N, in the direction in which the velocity changes. A box of mass 6.75 kg has a rope tied to it and it is being pulled along the floor. Its acceleration is m/s 2, west. What net force must be acting on it?

3 3 According to Newton s Second Law of motion, the rope and all the other things the box is in contact with (for example, the floor) must be exerting a net force on the box of a = (6.75 kg) x (0.100 m/s 2, west) = N, west. A kite is subject to a net force of N, northwest. Its acceleration is 2.35 m/s 2, northwest. According to Newton s Second Law (Eq. E3.4.1a), which is a vector relation, the directions of the net force on an object and acceleration of that object must be the same. Luckily, this appears true for this problem. If this were not so, it would have meant we had lost track of some of the forces that contribute to the change in motion. Any time you come on a case for which the net force and acceleration have different directions, you must have missed identifying at least one of the forces acting that contribute to the net force. What must the kite s mass be if these data are true? If mass is not known but force and acceleration are, the mass may be determined from the relation found as a consequence of Eq. E3.4.1b, a = F/m = (0.389 N)/(2.35 m/s 2 ) = kg. Note that we did not give the directions, because we knew that F and a were both in the same direction. The mass m is a scalar; it has no direction associated with it. Newton s Third Law of motion What causes a force? Forces do not just appear magically. Every force that is exerted on an object (call it object A) is the result of some other material agent acting on it to cause that force. Suppose object B touches object A or holds something that touches A. Because of the presence of B, there is a force acting on A.

4 4 Let s suppose Ashley and Beth are each standing still holding the ends of a rope. Beth pulls on Ashley. If Beth lets go, both Beth and Ashley will briefly struggle to regain their balance in other words, when they let the rope go, their motions will change. Letting go of the rope changes the forces that act; for example, Beth is no longer pulling on Ashley, who had braced herself to keep herself motionless. When Ashley s force is removed, she might briefly stagger before recovering. The fact that Beth has also to struggle indicates that the balance of Beth s forces changed, too, when she let the rope go. Where could that force that was suddenly removed have come from? The only thing that changed is that Ashley and Beth are no longer connected by the rope. Ashley must have been causing a force that acted on Beth. Newton recognized this fact if Ashley causes a force that acts on Beth, then reciprocally Beth causes a force that acts on Ashley. Furthermore, another simple experiment shows that the size of the forces must have been the same and that the forces had to act in opposite directions. Candace replaces the rope. Both Ashley and Beth pull. If Beth lets go, Candace and Ashley briefly move away from her (their motion had changed). They hold hands and pull again, then Ashley lets go. Now Candace and Beth briefly move away from her, in the direction opposite to that Candace and Ashley had moved). When they both pull on Candace, Candace doesn t move (she s not changing her motion). According to the First Law, the two forces on her (by Ashley and by Beth) are balanced. They must be the same size, but in opposite directions. So, if Ashley pulls on Beth, Beth must pull equally on Ashley, but in the opposite direction. Sometimes, these are referred to as action and reaction forces, but that is an

5 5 invitation to think that some forces are more fundamental, or precede other forces. The two forces (the force on Ashley caused by Beth and the force on Beth caused by Ashley in the rope example) act pairwise, with essentially no time lag. The two forces are acting on different objects, in distinction to the First and Second Laws, which refer to all the forces acting on ONE object.