Apparent weight The weight is read by a scale It is given by the magnitude of the normal force W′=|N|=N N >)The block pushes on the scale with a mg force equal but opposite to N(action reaction) The normal is found from the net force net=N+mg= ma If platform (and object+scale)is not accelerated Net force is zero N=-mg =,W=mg Physics 121: Lecture 5, Pg 6
Physics 121: Lecture 5, Pg 6 Apparent weight The weight is read by a scale It is given by the magnitude of the normal force »The block pushes on the scale with a force equal but opposite to N (actionreaction) If platform (and object+scale) is not accelerated Net force is zero N mg -N The normal is found from the net force a
Apparent weight N If the "elevator is accelerated a Net force≠0 net N+mg= ma g Choosing axis as illustrated N-mg=ma=>N=m(g +a) a Apparent weight is W′=m(g+a) N mg W>mg if a>0(upward): heavier W <mg if a>0(downward): lighter N Physics 121: Lecture 5, Pg 7
Physics 121: Lecture 5, Pg 7 Apparent weight If the “elevator” is accelerated Net force 0 Choosing axis as illustrated a N mg Apparent weight is W’ >mg if a>0 (upward): “heavier” W’ <mg if a>0 (downward): “lighter” a N mg -N
Chapter 4: Vectors In 1 dimension, we can specify direction with a or-sign In 2 or 3 dimensions, we need more than a sign to specify the direction of something To illustrate this, consider the position vector in 2 dimensions Example: Where is Boston? Choose origin at New York Boston Choose coordinate system Boston is 212 miles northeast of new york or New york Boston is 150 miles north and 150 miles east of new york Physics 121: Lecture 5, Pg 8
Physics 121: Lecture 5, Pg 8 Chapter 4: Vectors In 1 dimension, we can specify direction with a + or - sign. In 2 or 3 dimensions, we need more than a sign to specify the direction of something: To illustrate this, consider the position vector r in 2 dimensions. Example: Where is Boston? Choose origin at New York Choose coordinate system Boston is 212 miles northeast of New York or Boston is 150 miles north and 150 miles east of New York Boston New York r
Vectors There are two common ways of indicating that something is a vector quantity Boldface notation: A A=A Arrow notation: A Physics 121: Lecture 5, Pg 9
Physics 121: Lecture 5, Pg 9 Vectors... There are two common ways of indicating that something is a vector quantity: Boldface notation: A “Arrow” notation: A = A A
Vectors, definition A vector is composed of a magnitude and a direction examples: displacement, velocity, acceleration magnitude of A is designated Al usually carries units A vector has no particular position Two vectors are equal if their directions and magnitudes match A=C A≠B.B≠C Physics 121: Lecture 5, Pg 10
Physics 121: Lecture 5, Pg 10 Vectors: definition A vector is composed of a magnitude and a direction examples: displacement, velocity, acceleration magnitude of A is designated |A| usually carries units A vector has no particular position Two vectors are equal if their directions and magnitudes match. A B C A = C A = B, B = C