4 Dynamics: Newton’s Laws of Motion Dynamics Deals with Why objects move, what makes them start to move? What causes them to accelerate or decelerate? We will introduce force and the connection between force and motion 4.1 Force • Force -A push or pull that causes an object to move • An object at rest requires force to start to move, to change velocity, or to change direction • Forces have magnitude and direction, they are vectors • The same vector math for velocity applies to forces 4.2 Newton’s First Law of Motion • Newton’s First Law of Motion -Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it. • Basically, an object with no force acting on its will remain at rest or in motion • Inertia -An object’s tendency to maintain its state of rest or uniform velocity • Thus, Newton’s First Law is often called the Law of Inertia Inertial Reference Frames • Newton’s first law depends on the frame of reference – Example -To an outside observer the driver of an accelerating car is accelerating, but from inside the car, you are at rest • Inertial Reference Frames -A frame of reference from which Newton’s first law holds • For most purposes a fixed point on Earth serves as an inertial frame of reference • Noninertial Reference Frames -A frame of reference that does not adhere to Newton’s First Law, such as a frame of reference that is acceleration 4.3 Mass • Mass -Measure of inertia of an object, the more mass something has, the more it will resist a force • Also known as the quantity of matter an object has • The SI unit for mass is the kilogram (kg) • Weight is NOT the same as mass, weight measures the force of gravity an object experiences, weight is dependent on mas 4.4 Newton’s Second Law of Motion • Newton’s Second Law of Motion -The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to the object’s mass. The direction of the acceleration is in the direction of the force acting on the object • In equation form: Where a is acceleration, ΣF is the sum of the forces acting on an object, and m is the mass of the object. • Manipulating the equation to solve for the total force acting on an object gives • The sum of force on an object is also known as the net force • Net forces cause acceleration • Force -An action capable of accelerating an object • Force can be written in component form as ΣF x = max ΣF y = may 4.5 Newton’s Third Law of Motion • Newton’s Third Law of Motion -Whenever one object exerts a force on a second object, the second object exerts an equal force in the opposite direction of the first • A force always causes an equal and opposite force from the object being acted on – Example -A hammer on a nail causes the nail to exert an equal force in the opposite direction of the hammer • The equation for the force of object B on object A if A acts on B is F AB = −F BA 4.6 Weight -the Force of Gravity; and the Normal Force • Earth exerts on all objects on it, gravity, which is the same for all objects and acts downwards • The force of gravity of Earth on an object is represented by Where is the acceleration due to gravity of object on Earth, typically accepted to be • WHen two objects are in contact, they exert a contact force on each other • Normal Force -A contact force that is perpendicular to the common surface of two objects • When an object is on a surface, the object exerts a downward gravitational force on the surface and the surface exerts an upward normal force on the object • The normal force exerts by a surface on an object has the same magnitude as the gravitational force from the object, given by where m is the mass of the object and g is the acceleration due to gravity • Normal forces can also be cause when an object pushes on a surface horizontally instead of vertically 4.7 Solving the Problems with Newton’s Laws; Free-Body Diagram • Free=body Diagram -Also called a force diagram, this is a simple way to represent the forces acting on an object in order to determine the net force on it • Net Force -To review, this is a the vector sum of all the forces on an object • The object in question in a fre body diagram is treated as a point particle. That is, its size and dimensions are not taken into account Tension in a Flexible Cord • Tension -The force a flexible cord experiences when it is pulled on • We treat flexible cords as having ”negligible mass” or mass so little that it does not have ot be taken into account 4.8 Problems Involving Friction, Inclines Friction • The surfaces of objects are not perfectly smooth, they have small imperfections and bumps that cause them to catch on each other when they slide together, the resistance of movement caused by surfaces is called friction and is a force • Kinetic Friction -Friction between two surfaces in motion, represented by Fk = µkFN Where Fk is the force of kinetic friction, µk is the coefficient of kinetic friction between the two surfaces,and FN is the normal force between the two surfaces • Static Friction -Friction between two surfaces that are not in motion, represented by Fs ≤ µsFN Where Fs is the force of static friction and µs • Note that the coefficients of kinetic and statics friction for the same surfaces can and most likely will be different, usually µs will be greater than µk • The force of static friction scales with your push until the maximum force is reached, represented by Fs = µsFN , once this limit is surpassed, kinetic friction will take over Inclines • Objects on an incline experience the force of gravity as a pushing force resisted by friction • The normal force experienced by an object on an incline is given by FN = mg cos θ WHere θ is the angle of the incline. Since the force of gravity is at an angle relative to the normal force from the incline • The pushing force experienced by an object on an incline is given by Fp = mg sin θ Which is the other component of gravitational force