#### Transcript Newton’s Laws of Motion

Classroom Change Our class will be in Hamilton Hall 302 from now on ! Physics 1D03 - Lecture 6 1 Vector Review • Scalars and Vectors • Vector Components and Arithmetic Physics 1D03 - Lecture 6 2 Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units examples: mass, charge, energy . . . Vector : described by a scalar (its magnitude) and a direction in space examples: displacement, velocity, force . . . Vectors have direction, and obey different rules of arithmetic. Physics 1D03 - Lecture 6 3 Notation • Scalars : ordinary or italic font (m, q, t . . .) • Vectors : - Boldface font (v, a, F . . .) - arrow notation ( v, a, F . . .) - underline (v, a, F . . .) • Pay attention to notation : “constant v” and “constant v” mean different things! Physics 1D03 - Lecture 6 4 Coordinate Systems In 2-D : describe a location in a plane y • by polar coordinates : (x,y) distance r and angle r y • by Cartesian coordinates : 0 x x distances x, y, parallel to axes with: x=rcosθ y=rsinθ These are the x and y components of r Physics 1D03 - Lecture 6 5 Addition: If A + B = C , A Ay Ax B By Bx then: Cx Ax Bx Tail to Head Cy Ay By B C Cz Az Bz Three scalar equations from one vector equation! Cy Bx A Ax By Ay Cx Physics 1D03 - Lecture 6 6 Newton’s Laws of Motion • Newton’s Laws • Forces • Mass and Weight Physics 1D03 - Lecture 6 7 Newton’s First Law (Law of Inertia) An isolated object, free from external forces, will continue moving at constant velocity, or remain at rest. Earlier, Aristotle said objects were “naturally” at rest, and needed a continuing push to keep moving. Galileo realized that motion at constant velocity is “natural”, and only changes in velocity require external causes. Objects in equilibrium (no net external force) also move at constant velocity. Physics 1D03 - Lecture 6 8 Forces • A force is a push or pull that tends to cause motion (more exactly, changes in motion) • From the Second Law, force should have units of 1 kg m/s 2 1 newton (N) • Force is a vector. • In Newton’s dynamics, all influences on a particle from its surroundings are expressed as forces exerted on that particle. Physics 1D03 - Lecture 6 9 Newton’s Second Law Fnet ma Fnet (or Ftotal) is the vector sum of all forces acting on the particle of mass m: Fnet Fi mai i i The acceleration a is parallel to the total force, and proportional to it. The proportionality constant is the particle’s mass. Newton defines mass as a measure of an object’s inertia. Physics 1D03 - Lecture 6 10 Contact Forces : direct contact is required examples - normal forces, friction, air resistance, buoyancy, ... Non-Contact Forces : gravity, electromagnetic, weak and strong forces The gravitational force is also called weight and is measured in Newtons. Weight is proportional to mass : Fw = mg, where g is the gravitational field (and is also the acceleration of an object in free fall). Physics 1D03 - Lecture 6 11 Weight and Mass Weight is a force; it can be measured using a spring scale On Earth, a baseball weighs 2.40 N On the moon, a baseball weighs 0.40 N Physics 1D03 - Lecture 6 12 • Mass is a measure of inertia : on the earth or on the moon, a 24.5 N force applied to the baseball will give it an acceleration of 100 m/s2 (its mass is m = F/a = 0.245 kg) • We can compare masses with a balance, because of the remarkable property : weight mass Weights are equal when masses are equal Fg ,1 Fg,2 Physics 1D03 - Lecture 6 13 Newton’s Third Law (action and reaction) If object A exerts a force on object B, object B exerts an equal, opposite force back on A. Physics 1D03 - Lecture 6 14 Newton’s Third Law : examples What is the “reaction” to the following forces? Fg Fg Gravity (of block) pulls earth up Block pushes down on table You push on a block Balloon pushes on air outside Physics 1D03 - Lecture 6 15 Quiz A 140-kg wrestler and a 90-kg wrestler try to push each other backwards out of the ring. At first they are motionless as they push; then the large wrestler moves the other one backwards. Compare the forces they exert on each other. Which statement is correct? a) The forces are always equal. b) The larger wrestler always exerts a larger force. c) When they are motionless, the forces are equal; they start to move when the large wrestler exerts a larger force on his opponent than his opponent exerts back on him. Physics 1D03 - Lecture 6 16 Contact Forces Examples : A heavy block on a table • The table must push up on the block to prevent it from falling Forces on Block Fg • The type of contact force is called a normal force if it is perpendicular (normal) to the surfaces in contact. • The normal force will be as large as necessary to hold the block (until the table breaks) Ftable Physics 1D03 - Lecture 6 17 If we look closely, the normal force arises from the table being bent : as the table tries to straighten, it pushes back. This is really an elastic force; the table behaves like a spring. At the atomic level, all contact forces are due to electromagnetic forces. Physics 1D03 - Lecture 6 18 [email protected]%&*#$ We divide the contact force into two “components” Fg FA f n - normal force : n is perpendicular to the surfaces in contact - friction : f is parallel to the surface friction has a more complex behaviour than the normal force (next lecture) Physics 1D03 - Lecture 6 19