2Newton’s Laws of Motion Newton’s First Law of MotionEvery object will continue in a state of rest or with constant speed in a straight line unless acted upon by an external force.Newton’s Second Law of MotionWhen a net force act on an object, the object accelerates in the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass. Thus, a F/m or, a F/mNewton’s Third Law of MotionWhenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
3ForceA force is not a thing in itself but an interaction between one thing and another.Force is an interaction between two objects.Action force: hand on wallReaction force: wall on handYou can not push on somethingwithout being pushed back.
4ForceIf you push on a wall with your fingers, more is happening than you pushing on the wall.The wall is also pushing on you.How else can you explain the bending of your fingers?Your fingers and the wall push on each other.There is a pair of forces involved:your push on the wall andthe wall's push back on you.These forces are equal in magnitude and opposite in direction and comprise a single interaction.In fact, you can't push on the wall unless the wall pushes back.
5Who is pushingForce is an interaction between two objects. Action force: hand on wall Reaction force: wall on hand You can not push on something without being pushed back.
8ForceTension on the spring is 100 N N = 200 N As a whole the balance is not moving as it has two equal and opposite forces and they are canceling out. Any of these weight is not moving as the balance is pulling back with 100 N on each of them.
9ForceTension on the spring is 100 N. As a whole the balance is not moving as it has two equal and opposite forces and they are canceling out. Any of these weight is not moving as the balance is pulling back with 100 N on each of them.
10An interaction requires a pair of forces Consider a boxer's fist hitting a massive punching bag. Fist hits the bag (and dents it) while the bag hits back on the fist (and stops its motion). In hitting the bag there is an interaction with the bag that involves a pair of forces. The force pair can be quite large. An interaction requires a pair of forces acting on two objects.
11An interaction requires a pair of forces But what if hitting a piece of tissue paper? The boxer's fist can only exert as much force on the tissue paper as the tissue paper can exert on the fist. Furthermore, the fist can't exert any force at all unless what is being hit exerts the same amount of force back. An interaction requires a pair of forces acting on two objects.
12Other examples: You pull on a cart and it accelerates. But in doing so, the cart pulls back on you, as evidenced perhaps by the tightening of the rope wrapped around your hand.One thing interacts with another;you with the cart
13Other examples: A hammer hits a stake and drives it into the ground. In doing so, the stake exerts an equal amount of force on the hammer, which brings the hammer to an abrupt halt.One thing interacts with another;you with the cart, orthe hammer with the stake.
14Newton's 3rd Law of Motion Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
15Examples of Newton’s 3rd Law The hand exerts an action force on the putty.The putty changes shape.The putty exerts a reaction force on the hand.The hand also changes shape.
16Examples of Newton’s 3rd Law Try standing on a skateboard Facing a partner on another skateboard with equal masses.Give your partner a gentle push. What happens?The partner accelerates away from you.The partner exerts a reaction force on you.You also accelerate in the opposite direction.Both of you move even though one person pushed the other.Thus both an action and reaction force exists.
17Examples of Newton’s 3rd Law Through the ball away from you.As you exert a force forward on the ball, you accelerate backward.The ball must exert a reaction force back on you.Similar to a rocket.
18Examples of Newton’s 3rd Law In order to move, the rocket expels gaseous molecules. The rocket exerts a large force on the molecules to expel them at a very high speed. At the same time, the gaseous molecules exert a forward force of equal magnitude on the rocket.Expelled molecules do not need to push against the ground or the atmosphere to propel the rocket.If it was the case, the rocket would not accelerate in the vacuum of outer space.
19Newton's 3rd Law of Motion Newton's third law is often stated thus: “To every action there is always opposed an equal reaction.” In any interaction there is an action and reaction pair of forces that are equal in magnitude and opposite in direction. Neither force exists without the other—forces come in pairs, one action and the other reaction. The action and reaction pair of forces makes up one interaction between two things.
20Defining Your SystemAn interesting question often arises; since action and reaction forces are equal and opposite, why don't they cancel to zero? To answer this question we must consider the system involved. Consider the force pair between the apple and orange. A force is exerted on the orange by the apple and the orange accelerates.
21Defining Your SystemWe'll first consider the system to be the orange, and define it by a dashed line surrounding it. Note that there is an external force acting on the system—which is provided by the apple. The fact that the orange simultaneously exerts a force on the apple, which is external to the system, may affect the apple (another system), but not the orange. The force on the orange is not canceled by the force on the apple. So in this case the action and reaction forces don't cancel.When the orange is the system (within the dashed line) an external force provided by the apple acts on it.Action and reaction forces do not cancel and the system accelerates.
22Defining Your SystemIf, however, we consider the system to enclose both the orange and apple, the force pair is internal to the orange-apple system. Then the forces do cancel each other. The apple and orange move closer together but the system's “center of gravity” is in the same place before and after the pulling. There is no net force and therefore no net acceleration. Relatively they are not moving. Similarly, the many force pairs between molecules in a golf ball may hold the ball together into a cohesive solid, but they play no role at all in accelerating the ball. A force external to the ball is needed to accelerate the ball.When both the orange and apple compose the system (both within the dashed line) no external force acts on it. Action and reaction are within the system and do cancel to zero. Zero net force means no acceleration of the system.
23Defining Your Systemthe system enclosed both the orange and apple can only move if there is an external force. That external force may be when the floor pushes back on the apple.An external horizontal force occurs when the floor pushes on the apple (reaction to the apple’s push on the floor).The orange-apple system accelerates.
24Defining Your System Newton’s Second Law of Motion Newton’s 2nd law describes the effect of forces on a single object.Newton’s 3rd law describes the effect of forces between two objects.Newton’s Second Law of MotionWhen a net force act on an object, the object accelerates in the direction of the net force. The acceleration is directly proportional to the net force and inversely proportional to the mass. Thus, a F/m or, a F/mNewton’s Third Law of MotionWhenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.Remember the action and reaction forces are on the different objects.
25Defining Your SystemIn general, when Body A inside a system interacts with Body B outside the system, each can experience a net force. Action and reaction forces don't cancel. You can't cancel a force acting on Body A with a force acting on Body B. Forces cancel only when they act on the same body, or on the same system. Action and reaction forces always act on different bodies.
26Action and Reaction on Different Masses As strange as it may first seem, a falling object pulls upward on the Earth as much as the Earth pulls downward on it. The downward pull on the object seems normal because the acceleration of 10 meters per second each second is quite noticeable. The same amount of force acting upward on the huge mass of the Earth, however, produces acceleration so small that it cannot be noticed or measured.
27When a ball drops on the earth The action force that the earth exerts on the ball is equal in size , but opposite in direction, to the reaction force that the ball exerts on the Earth. The reason we see the acceleration of the ball, but not the earth, is because the ball has less mass than the Earth.
28Action and Reaction on Different Masses The role of different masses is evident in a fired rifle. When firing a rifle there is an interaction between the rifle and the bullet. A pair of forces acts on both the rifle and the bullet. The force exerted on the bullet is as great as the reaction force exerted on the rifle; hence, the rifle kicks back. Since the forces are equal in magnitude, why doesn't the rifle recoil with the same speed as the bullet?
29Action ReactionIn analyzing changes in motion, Newton's second law reminds us that we must also consider the masses involved. Suppose we let F represent both the action and reaction force, m the mass of the bullet, and the mass of the more massive rifle. The accelerations of the bullet and the rifle are then found by taking the ratio of force to mass. The acceleration of the bullet is given by while the acceleration of the recoiling rifle is We see why the change in motion of the bullet is so huge compared to the change of motion of the rifle.
30RocketIf we extend the idea of a rifle recoiling or “kicking” from the bullet it fires, we can understand rocket propulsion. Consider a machine gun recoiling each time a bullet is fired. If the machine gun is fastened so it is free to slide on a vertical wire, it accelerates upward as bullets are fired downward.
31RocketA rocket accelerates the same way. It continually “recoils” from the ejected exhaust gas. Each molecule of exhaust gas is like a tiny bullet shot from the rocket.
32RocketConsider a balloon recoiling when air is expelled. If the air is expelled downward, the balloon accelerates upward.
45Summary of Newton's Three Laws An object at rest tends to remain at rest; an object in motion tends to remain in motion at constant speed along a straight-line path. This tendency of objects to resist change in motion is called inertia. Mass is a measure of inertia. Objects will undergo changes in motion only in the presence of a net force. When a net force acts on an object, the object will accelerate. The acceleration is directly proportional to the net force and inversely proportional to the mass. Symbolically, a = F/m. Acceleration is always in the direction of the net force. When objects fall in a vacuum, the net force is simply the weight, and the acceleration is g (the symbol g denotes that acceleration is due to gravity alone). When objects fall in air, the net force is equal to the weight minus the force of air resistance, and the acceleration is less than g. If and when the force of air resistance equals the weight of a falling object, acceleration terminates, and the object falls at constant speed (called terminal speed). Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force of the first. Forces come in pairs, one action and the other reaction, both of which comprise the interaction between one object and the other. Action and reaction always act on different objects. Neither force exists without the other.
46VectorsAny quantity that requires both magnitude and direction for a complete description is a vector quantity. Examples of vector quantities include force, velocity, and acceleration. A quantity that can be described by magnitude only, not involving direction, is called a scalar quantity. Mass, volume, and speed are scalar quantities. A vector quantity is nicely represented by an arrow. When the length of the arrow is scaled to represent the quantity's magnitude, and the direction of the arrow shows the direction of the quantity, we refer to the arrow as a vector.
47VectorsAdding vectors that act along parallel directions is simple enough: if they are in the same direction, they add; if they are in opposite directions, they subtract. The sum of two or more vectors is called their resultant.
48VectorsTo find the resultant of two vectors that don't act in exactly the same or opposite direction, we use the parallelogram rule. Construct a parallelogram wherein the two vectors are adjacent sides - the diagonal of the parallelogram shows the resultant. In Figure the parallelograms are rectangles.
49VectorsWhen two equal-length vectors at right angles to each other are added, they form a square. The diagonal of the square is the resultant, √2 times the length of either side.
50Force VectorsOne is 30 newtons and the other is 40 newtons. Simple measurement shows the resultant is 50 newtons
51Which rope has the greater tension? Nellie Newton hanging at rest from a pair of ropes that make different angles with the vertical.Investigation will show there are three forces acting on Nellie:her weight,a tension in the left-hand rope, anda tension in the right rope.Because the ropes hang at different angles, the rope tensions will be different from each other.
52a step-by-step solution Because Nellie hangs in equilibrium, her weight must be supported by tensions in the ropes, which must add vectorially to equal her weight. Use of the parallelogram rule shows that the tension in the right-hand rope is greater than the tension in the left rope. If you measure the vectors you'll see that tension in the right rope is about twice the tension in the left rope. How does tension in the right rope compare with her weight?
53Velocity VectorsSpeed is a measure of “how fast”; velocity is a measure of both how fast and “which direction.” If the speedometer in a car reads 100 kilometers per hour you know your speed. If there is also a compass on the dashboard, indicating that the car is moving due north, for example, you know your velocity—100 kilometers per hour north. To know your velocity is to know your speed and your direction.
54Velocity VectorsConsider an airplane flying due north at 80 kilometers per hour relative to the surrounding air. Suppose that the plane is caught in a 60-kilometer-per-hour crosswind (wind blowing at right angles to the direction of the airplane) that blows it off its intended course. Velocity vectors scaled so that 1 centimeter represents 20 kilometers per hour. Thus, the 80-kilometer-per-hour velocity of the airplane is shown by the 4-centimeter vector and the 60-kilometer-per-hour tailwind is shown by the 3-centimeter vector.The diagonal of the constructed parallelogram (rectangle in this case) measures 5 cm, which represents 100 km/h. So the airplane moves at 100 km/h relative to the ground, in a direction northeast.
55resulting velocitiesHere we see a top view of an airplane being blown off course by wind in various directions. With pencil and using the parallelogram rule, sketch the vectors that show the resulting velocities for each case. In which case does the airplane travel fastest across the ground? Slowest?
56Components of VectorsJust as two vectors at right angles can be combined into one resultant vector, in reverse any vector can be “resolved” into two component vectors perpendicular to each other. These two vectors are known as the components of the given vector they replace. The process of determining the components of a vector is called resolution. Any vector drawn on a piece of paper can be resolved into a vertical and a horizontal component.
57Vector resolutionA rectangle is drawn that has V as its diagonal. The sides of this rectangle are the desired components, vectors X and Y. In reverse, note that the vector sum of vectors X and Y is V.
58Resultant velocity ?Consider a motorboat that normally travels 10 km/h in still water. If the boat heads directly across the river, which also flows at a rate of 10 km/h, what will be its velocity relative to the shore?
59Resultant velocity ?Consider a motorboat that normally travels 10 km/h in still water. If the boat heads directly across the river, which also flows at a rate of 10 km/h, what will be its velocity relative to the shore?
60Then answer these questions Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same water flow. Construct resultant vectors showing the speed and direction of the boats.Which boat takes the shortest path to the opposite shore?(b) Which boat reaches the opposite shore first?(c) Which boat provides the fastest ride?
61Components of VectorsWith a ruler, draw the horizontal and vertical components of the two vectors shown. Measure the components and compare your findings with the answers given below. (Left vector: the horizontal component is 3 cm; the vertical component is 4 cm. Right vector: the horizontal component is 6 cm; the vertical component is 4 cm.)