Chapter 4: Dynamics: Newton's Laws of Motion PDF

Chapter 4:Dynamics : Newtons Laws of Motion Mrs. Pooja Brahmaiahchari Introduction The study of motion is kinematics, but kinematics only describes them way objects move—their velocity and their acceleration. Dynamics considers the forces that affect the motion of moving objects and s...

Chapter 4:Dynamics : Newtons Laws of Motion Mrs. Pooja Brahmaiahchari Introduction The study of motion is kinematics, but kinematics only describes them way objects move—their velocity and their acceleration. Dynamics considers the forces that affect the motion of moving objects and systems. Newton’s laws of motion are the foundation of dynamics. Isaac Newton’s (1642–1727) laws of motion were just one part of the monumental work that has made him legendary. 4.1 Force Force—that is, a push or a pull. Push or Pull has both magnitude and direction (therefore, it is a vector quantity). If two people push in different directions on a third person, as illustrated in Figure, we might expect the total force to be in the direction shown. Since force is a vector, it adds just like other vectors, as illustrated in Figure(a) for two ice skaters. In figure (b) The body is represented by a single isolated point (or free body), and only those forces acting on the body from the outside (external forces) are shown. 4.2 Newton’s First Law of Motion Newton’s First Law of Motion states that, “A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force”. Newton’s first law of motion states that there must be a cause (which is a net external force) for there to be any change in velocity. Newton’s first law is completely general and can be applied to anything from an object sliding on a table to a satellite in orbit to blood pumped from the heart.  The property of a body to remain at rest or to remain in motion with constant velocity is called Inertia. Newton’s first law is often called the Law of Inertia. The Inertia of an object is measured by its mass. The quantity or amount of matter in an object is determined by the numbers of atoms and molecules of various types it contains. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon. Mass always remains the same. Which has more mass: a kilogram of cotton balls or a kilogram of gold? Ans: They are equal. A kilogram of one substance is equal in mass to a kilogram of another substance. The quantities that might differ between them are volume and density. 4.3 Newton’s Second Law of Motion It mathematically states the cause-and-effect relationship between force and changes in motion. Newton’s second law of motion is more quantitative and is used extensively to calculate what happens in situations involving a force. What is meant by change in motion ? Change in motion is equivalent to a change in velocity. A change in velocity means, by definition, that there is an acceleration. Newton’s first law says that a net external force causes a change in motion; thus, we see that a net external force causes acceleration.  An external force acts from outside the system of interest. In figure (a) the two forces exerted by the other children are external forces. An internal force acts between elements of the system. Only external forces affect the motion of a system, according to Newton’s first law. You must define the boundaries of the system before you can determine which forces are external.  In figure (b) All of the external forces acting on the system add together to produce a net force 𝐹𝑛𝑒𝑡. The free-body diagram shows all of the forces acting on the system of interest. In (c) A larger net external force produces a larger acceleration (a’ > a ) when an adult pushes the child. It seems reasonable that acceleration should be directly proportional to F and in the same direction as the net (total) external force acting on a system. Acceleration should be inversely proportional to the mass of the system. In other words, the larger the mass (the inertia), the smaller the acceleration produced by a given force.  The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newton’s second law of motion is 𝐹𝑛𝑒𝑡 𝑎= 𝑚 This is often written in the more familiar form 𝐹𝑛𝑒𝑡 = ma The SI unit of force is called the Newton (abbreviated N) 1. Suppose that the net external force exerted on a lawn mower is 62 N parallel to the ground. The mass of the mower is 24 kg. What is its acceleration? Weight and gravitational force When object is dropped, the net force on a falling object is the gravitational force, commonly called its weight. Weight is a measure of the gravitational force exerted on an object. weight changes when gravity changes. It depends on the location Weight is a vector because it has a direction; down; by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as w. Hence, 𝑤 = 𝑚𝑔 When the net external force on an object is its weight, we say that it is in free-fall. Difference between Mass and weight Mass Weight Mass is a measure of how much matter is Weight is a measure of the force of in an object. gravity acting on an object. Mass is measured in terms of kilograms. Weight is measured in terms of Newtons. Mass of the object Remains Same Weight of an object changes 2. The weight of an astronaut plus his space suit on the Moon is only 250 N. How much do they weigh on Earth? What is the mass on the Moon? On Earth? (given acceleration due to gravity on moon g is 1.625 m/s2 ). 4.4 Newton’s Third Law of Motion Newton’s Third Law of Motion states that, “Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts.” We sometimes refer to this law loosely as “action-reaction,” where the force exerted is the action and the force experienced as a consequence is the reaction. Normal Force Normal force is the force of contact between two objects. It is called normal force because the force always acts perpendicular to the surface of contact. Usually, we will pick our coordinate system with the standard Cartesian alignment. For some problems it is convenient to align the coordinate system with the direction of motion. The most convenient coordinate system for motion on an incline is one that has one coordinate parallel to the slope and one perpendicular to the slope. 3. Consider the skier on a slope shown in Figure. Her mass including equipment is 60.0 kg. (a) What is her acceleration if friction is negligible? (b) What is her acceleration if friction is known to be 45.0 N? Tension Tension is the force conveyed by a flexible medium, usually a rope or a cord. The word “tension” comes from a Latin word meaning “to stretch.” Newton’s 3rd law applies to tension meaning that a rope pulling on one object pulls in the opposite direction somewhere else. You CANNOT push on a rope…!!  Tension in the rope must equal the weight of the supported mass, as we can prove using Newton’s second law. The only external forces acting on the mass are its weight w and the tension T supplied by the rope. Thus, 𝐹𝑛𝑒𝑡 = 𝑇 − 𝑤 = 0 Where T and w are the magnitudes of the tension and weight and their signs indicate direction, with up being positive here. Thus, just as you would expect, the tension equals the weight of the supported mass: T = w = mg 4. A rope is used to lift a 50kg box with upward acceleration of 2.3 m/s2. a) What is the tension in the rope? b) What would be the tension, if box descend slowly with downward acceleration of 0.75 m/s2. 5. What is the tension in two ropes shown in figure. 6. Calculate the tension in two ropes shown below Real Forces and Inertial Frames Real forces are those that have some physical origin, such as the gravitational pull. Contrastingly, fictitious forces are those that arise simply because an observer is in an accelerating frame of reference, such as one that rotates. For example, if a satellite is heading due north above Earth’s northern hemisphere, then to an observer on Earth it will appear to experience a force to the west that has no physical origin. An inertial frame of reference is one in which all forces are real and, equivalently, one in which Newton’s laws have the simple forms given. Earth’s rotation is slow enough that Earth is nearly an inertial frame. THANK YOU