Newton s Laws Review THE SCIENCES OF MOTION Prior to this unit, we had been studying, which is the science of describing motion with words, numbers, pictures, and symbols, and no attention was given to the of the motion. In this unit, we turned our attention to, which is the study of the causes of motion, and unbalanced forces in particular. Both kinematics, dynamics, and statics (the study of objects being acted upon by balanced forces) all combine to form the science of, the interaction between matter and forces acting upon it. THE HISTORY OF NEWTON S LAWS OF MOTION (384-322 BC) developed the earliest theory of motion. He was one of the first s because he actually made observations upon which he drew conclusions (i or h ). Prior to Aristotle, science was nothing more than p aimed at the outside world. Aristotle did not run e as we think of them however. Aristotelian Physics was developed on the premise that all things were made of f e, but these differed from our present day ones. Aristotle said all earthly objects were made of a combination of,,, and. A fifth element, e, existed too; it was the building block of all objects in the heavens. As such it was perfect and incorruptible. The earthly elements had a natural order, which went from the bottom up,,, and. Aristotle thought that nature sought to maintain this natural order. Aristotle said when an object found itself outside of its naturally ordered place, it would desire to return to its natural home. This desire was so great that given the chance to go home, and object would move there on its own. This motion, which would seemingly happen all by itself, Aristotle called motion. The important thing about this motion was the happening all by itself part. Aristotle said that no agent (, as we would call it) was required to sustain this motion. Aristotle went on to say that motion that was not natural was v motion. This motion was imposed motion by an agent ( ), like a person or animal, which did not result in an object being back in its natural place after its completion. This motion would not happen on its own. In Aristotle s physics, a third type of motion was the motion of the heavenly bodies in perfect circles around the earth. This motion was named motion.
There were problems with Aristotelian physics that even occurred to Aristotle himself. First, p did not seem to obey the circular orbit idea. Next, two objects of different mass, but similar shape will fall at the, even though the heavier one should want to reach the earth more. Finally, an object thrown or fired, like a rock or an arrow, will continue to cover a great horizontal distance without the benefit of an applied force, and do not directly return to the ground when given the chance. These problems were largely ignored and not rectified. Despite its problems, Aristotle s physics was widely accepted through the 1600 s AD. It was so popular for a few reasons: it supported the earth-centered ( -centric) view of the universe that was so prevalent during the times; the idea that a is required to sustain horizontal motion seems to make sense in the real world and is consistent with everyday observation; and Aristotle was Aristotle-the leading authority on motion. In the early 1500 s, Nicolaus C began to notice that the mathematical model of the universe comes out a lot simpler if you assume the sun is the center of the universe, rather than the Earth. This view of the universe is called a h -centric model. This theory contains a moving earth, which hindered its acceptance since the prevailing thought is violent motion is caused by forces, and what could exert such a force? Copernicus work on motion was built upon my G, who faced much persecution, even ten years for his work in motion and the universe. Galileo developed many strategies that scientists use as second nature today. Galileo liked Aristotle s stance of making observations and hypotheses, but Galileo was the first to realize that must also be done to test the hypotheses. Galileo was also the first to take small details out of an experiment to see the main idea. Today, we call this an experiment. Galileo was also one of the first to use q methods, which involves associating numbers with measurements. These techniques make Galileo the father of the s m. Galileo ran a very important experiment. Galileo had a ramp with a downward incline followed by an upward incline with equal slope (like the picture on the left). He noticed that a ball would roll down the first incline and up the second incline to a height ALMOST the same as it was released. Galileo attributed this difference in height to. If friction could be eliminated, Galileo theorized that the ball would roll to the same height. This would be true even if the upward incline were of lesser slope (like the right picture); the ball would just have to cover more incline distance to reach the original height.
Finally, Galileo understood that if the second incline had no slope at all, the ball would never reach its original height. It would continue to roll. This understanding was monumental; for the first time in history, it was proposed that a force was not necessary to keep something moving that was moving in the first place. The object could continue to move on its own, if friction could somehow be eliminated. About the same time, Rene Descartes made an extreme idealization: what if friction and could be eliminated? In this friction-free, gravity-free environment, an object which was not moving would remain not moving unless a force caused it to change its state of motion. Also, in this environment, an object which was already moving would continue to move in a straight line at constant speed, unless a force caused it to change its state of motion. These ideas about the motion of objects became known as the Law of I. Descartes said that is a property of an object, proportional to the object s, that causes an object to changes in its state of motion.
In the 17 th century, wrote the world s first book, The P. In it, Newton outlined three laws of motion. They are: 1. Law of Bodies at tend to stay at. Bodies in tend to stay in. These rules hold unless an acts upon the body. Basically, this says f change v (cause a ). 2. Law of Acceleration is proportional to mass and proportional to. This can be ly stated as : Basically, this says the as the Law of Inertia. The Law of Acceleration is qu while the Law of Inertia is qu. 3. Law of For every, there is an and. This means, forces always come in. Some non-physics types think that since action and reaction are equal and opposite (like +5N and -5N), they will each other out. This is incorrect however; action and reaction will always be on, and consequently, could never cancel out. An confusing example of action and reaction comes from the gravitational force on an object, say a hot dog. If one asked, What is the reaction to gravity?, a wrong answer is likely. However, gravity is really the force of the on the. If this is the action, then the reaction
is obtained by simply switching the objects in the interaction: the force of the hot dog on the earth. If the hot dog weights 2 N, then the e F h = -2 N, while the hf e = +2 N. One might ask, If the forces are equal, why don t we get equal? This would imply the earth rising up toward the hot dog the same as the hot dog drops to the earth. The answer lies in the difference in. While it is true the forces are the same strength, the small mass of the hot dog allows this force to be very effective in accelerating the hot dog. Conversely, this same force is rendered PRACTICALLY useless by the gigantic mass of the earth. The word practically is important since even though the effect of the small force on the huge mass is slight, there still is an force, and consequently, there still is an, however miniscule. The key idea here is: there can be a big difference between a and its. A force = a or a. A force also = an between two objects. There are really two types of forces: 1. Contact Forces-forces in which the two interacting objects are. 2. -at-a- Forces-forces in which the two interacting objects are not actually touching. *see your Types of Forces Handout for more on these forces. Mass is a property of an object. We say this because it does not depend on the object s. Weight is different. Weight is the of on an object. Weight depends on, but is independent of. Weight can be easily calculated given the mass and the acceleration due to gravity at a given location. =
If mass is given in kilograms, and g is given in m/s/s, then the unit on weight is kg m/s/s. This cumbersome unit is nicknamed the. Volume is different still. Volume is the amount of an object takes up. An example of something with big mass but small volume is: An example of something with small mass but big volume is: The net force is the force an object. It is the r of all the forces on the object. A net force causes acceleration. Net force and acceleration will always be in the. To determine the net force, draw a - diagram (a picture of all the forces acting on an object). From this picture, pick a direction to be positive and the opposite direction to be negative. (In class, we usually pick the direction of the to be positive, but this is only for convenience; you could pick either direction and still get the correct answer.) The net force will be the positive forces added together and then the negative forces subtracted from this sum. For example, if right is considered positive in this picture, the net horizontal force (ΣF x ) =. For example, if up is considered positive in this picture, the net vertical force (ΣF y ) = F N F friction F app F t F g 1F 2 Newton s second law says that the net force (ΣF) = m a.
FRAME OF REFERENCE Remember frame of reference is the set of objects in your surroundings that are not moving relative to. These things are not getting or from you at the present time. frames of reference are ones that are not. An inertial frame of reference could be at rest, or it could be moving at speed. said that these frames of reference are. That is, the Newton s Laws pertain to both reference frames equally. Moreover, if you were in an inertial frame of reference on earth or in an identical inertial frame of reference aboard a spaceship moving with constant velocity, there is no way to discern which is which without looking outside the frame of reference. Moreover, there is no experiment which can be done to detect the constant motion. A non-inertial reference frame is different. A non-inertial reference frame is one that is being. Examples might be an accelerating car or an accelerating elevator. The Law of Inertia does not pertain to these reference frames. For instance, when aboard an accelerating car, you will feel the force the seat applies to your body. You can detect this unbalanced force. However, relative to things inside the car (things in your frame of reference) you remain at rest. Here, an object being acted upon by an unbalanced force should accelerate out of its frame of reference, but you do not move relative to the other items in the car. You are in a non-inertial reference frame. Another example is an accelerating elevator. Depending on whether an elevator is accelerating upward or downward, the rider s weight will seem to change. With upward acceleration and upward velocity, the rider will experience a sensation of being than normal. We say that the rider s weight is more than the rider s actual weight. Similarly, with downward acceleration and upward velocity, the rider will experience a sensation of being than normal. We say that the rider s apparent weight is less than the rider s actual weight. Drawing a free-body diagram of the rider in each case will show this. All objects free-fall the same because they have equal f to m ratios. Air resistance changes the a of a falling object. When air resistance =, we get, during which acceleration = is a force that motion. The three kinds of friction are: 1. 2. 3.
of is the number that describes the roughness or smoothness of a surface. The rougher the surface, the the µ. Smooth surfaces have µ s closer to. There are two kinds of sliding friction: 1. 2. Kinetic friction will be or equal to static friction, because it s easier to something moving than to something moving. Sliding friction also depends on, as seen in the equation: f =
ANSWERS kinematics cause dynamics mechanics Aristotle scientists inferences hypotheses philosophy experiments four elements earth water wind (air) fire ether earth water wind (air) fire Natural force Violent force Celestial planets same rate geo force Copernicus helio Galileo house arrest experiments idealizing quantitative scientific method friction forever gravity Inertia inertia directly mass resist Isaac Newton physics Principia Inertia rest rest motion motion unbalanced force forces velocity accelerations Acceleration inversely directly net force elegantly F net = ma (or Σ F = ma) same thing quantitative qualitative Force Pairs action equal opposite reaction pairs cancel different objects earth hot dog accelerations masses unbalanced acceleration force (or thing) effect push pull interaction touching Action Distance fundamental environment force gravity location mass location W = mg Newton space lead statue of Elvis Presley balloon shaped like Gumby one feels resultant same direction free-body acceleration F app + F t - F friction F N - F g - 1 F 2 you closer further Inertial accelerating constant Einstein equivalent accelerating heavier apparent lighter force mass acceleration weight terminal velocity zero Friction Resists Sliding Rolling Fluid Coefficient Friction higher zero Static Kinetic (sliding) less than keep start normal force f = µ F N
Some additional relevant problems: A person is standing on an scale, resting on a crate on another scale in an elevator. The person has a mass of 75 kg, and the crate weighs 1500. N. What does each scale read when: (answers) The elevator is stopped? (735N; 2235N) The elevator is moving with a constant velocity of 3.0 m/s upward? (735N; 2235N) s c a l e The elevator is accelerating upward at 1.5 m/s/s? (850N; 2580N) The elevator is accelerating downward at 4.5 m/s/s? (400N; 1210N)
a = 2.0 m/s/s Object B (mass of 2.30 kg) is sitting on an inclined plane, oriented at an angle of 40.0º. A mass of.70 kg is attached via a string and pulley to Object B. Determine the coefficient of kinetic friction between Object B and the plane. (.094) B 40.0º
Object A is on a horizontal frictionless surface. Object A weighs 4.9-N. A string is attached to it, which runs over a pulley and is attached to a.20-kg mass as shown. What is the acceleration of Object A? (2.8 m/s/s cw) A
Object J (mass of 6.50 kg) is sitting on an inclined plane, oriented at an angle of 62.0º. The coefficient of kinetic friction is 0.450 and the coefficient of static friction is 0.600 between Object J and the plane. Will Object J slide down the incline? (yes) J 62.0º If so, what will its acceleration be? (6.58 m/s 2 down incline)