Lecture 4: Dynamics: The Laws of Motion PDF

Lecture 4 Dynamics: The Laws of Motion Dr. Eman Moneer Introduction In previous Chapters, we described the motion of an object in terms of its position, velocity, and acceleration without considering what might influence that motion. Now we co...

Lecture 4 Dynamics: The Laws of Motion Dr. Eman Moneer Introduction In previous Chapters, we described the motion of an object in terms of its position, velocity, and acceleration without considering what might influence that motion. Now we consider that influence: Why does the motion of an object change? What might cause one object to remain at rest and another object to accelerate? Why is it generally easier to move a small object than a large object? The two main factors we need to consider are the forces acting on an object and the mass of the object. In this chapter, we begin our study of dynamics by discussing the three basic laws of motion, which deal with forces and masses and were formulated more than three centuries ago by Isaac Newton. Force and Motion Dynamics in Physics is the study of what can cause an object to accelerate. That cause is a Force, which is, loosely speaking, a push or pull on the object. The force is said to act on the object to change its velocity. Motion is when an object moves from one place to another, while force is what causes an object to move or to stop moving. Examples of force include the kick that causes a ball to move across the field and the gravity that slows and eventually stops that ball from moving. Newtonian Mechanics The study of that relation, as Newton presented it, is called Newtonian mechanics. We shall focus on its three primary laws of motion. Newtonian mechanics does not apply to all situations. If the speeds of the interacting bodies are very large we must replace. Newtonian mechanics with Einstein’s special theory of relativity, which holds at any speed, including those near the speed of light. If the interacting bodies are on the scale of atomic structure, we must replace Newtonian mechanics with quantum mechanics.  The Forces types … A force is commonly imagined as a push or a pull on some object. We can control the magnitude of the applied force and also its direction, so force is a vector quantity, just like velocity and acceleration. Contact forces, so named because they result from physical contact between two objects Field forces: Another class of forces doesn’t involve any direct physical contact.  Weight The magnitude of the gravitational force acting on an object of mass is called the weight of the object, given by:  The normal Force When a body presses against a surface, the surface deforms and pushes on the body with a normal force that is perpendicular to the surface. Tension Force When a cord (or a rope, cable, or another such object) is attached to a body and pulled tautly, the cord pulls on the body with a force T directed away from the body and along the cord (Fig.). The force is often called a tension force because the cord is said to be in a state of tension. To Summarize: Newton’s Laws The Vector Nature of Force 1. Newton’s First Law and Inertial Frames Newton’s First Law: If no force acts on a body, the body’s velocity cannot change; that is, the body cannot accelerate. In other words, if the body is at rest, it stays at rest. If it is moving, it continues to move with the same velocity (same magnitude and same direction).  When two or more forces act on a body, we can find their net force, or resultant force, by adding the individual forces vectorially. A single force that has the magnitude and direction of the net force has the same effect on the body as all the individual forces together. This fact is called the Principle pf superposition for forces Newton’s First Law is in terms of a net force can be states as: Mass and Inertia The tendency of an object to continue in its original state of motion is called inertia. Mass is a measure of the object’s resistance to changes in its motion due to a force. OR The mass of a body is the characteristic that relates a force on the body to the resulting acceleration. The SI unit of mass is the kilogram. Mass is a scalar quantity. Newton’s Second Law Like other vectors net force is equivalent to three component equations, one for each axis of an x y z coordinate system:  To solve problems with Newton’s second law, we often draw a free-body diagram in which the only body shown is the one for which we are summing forces. A system consists of one or more bodies, and any force on the bodies inside the system from bodies outside the system is called an external force. Internal forces that is, forces between two bodies inside the system. Check your understanding … The Gravitational Force and Weight Mass & Weight on the Moon Check your understanding … We can write Newton’s second law for the gravitational force in these vector forms: Newton’s Third Law Two bodies are said to interact when they push or pull on each other- that is when a force acts on each body due to the other body. Example 2 Analysis Models Using Newton’s Second Law Example 3 Example 4 Friction Force If we either slide or attempt to slide a body over a surface, the motion is resisted by a bonding between the body and the surface. The resistance is considered to be a single force called either the frictional force or simply friction. For Example … For Example … Example 1 Example 5 End of Lecture 4