Physics 101: Lecture 5, Pg 1 Free Fall and Apparent Weight Physics 101: Lecture 05 l Today’s lecture will cover Textbook Sections 4.3,4.5 Exam I Iclicker points are now in Gradebook! Please check that your scores were correctly recorded. Alexey Bezryadin will sub on Monday (and shoot the monkey!)

Physics 101: Lecture 5, Pg 2 Review from Lecture 4 Constant Acceleration Equations of Motion  x = x 0 + v 0 t + 1/2 at 2  v = v 0 + at  v 2 = v a(x-x 0 )  F = m a – Draw Free Body Diagram – Write down equations – Solve Today look at Gravity as force 05

Physics 101: Lecture 5, Pg 3 Free Fall l Only force acting on object is GRAVITY  Newton’s 2 nd Law  F y = ma y è Force is Weight = mg (near surface of earth) »  F y = ma y »-mg = ma y »a y = -g (- sign tells us it is in –y direction or down). l Acceleration is ALWAYS g downwards è Position may be positive, zero or negative è Velocity may be positive, zero or negative è Acceleration is always g downwards y x  y = y 0 + v y0 t - 1/2 gt 2  v y = v y0 - gt  v y 2 = v y g(y-y 0 ) 10

Physics 101: Lecture 5, Pg 4 Free Fall l Only force acting on object is GRAVITY l Acceleration is ALWAYS g downwards l Which will hit the ground first? A) Ball B) Same C) Feather y x 13 Note: Free fall only works when air resistance is negligible!

Physics 101: Lecture 5, Pg 5ACT l The speed of an object in free fall (Neglect Air Resistance) A. Always increases. B. is constant. C. Always decreases. D. May increase or decrease or be constant. E. May increase or decrease but is never constant. a = -g. Velocity becomes more and more negative. If v > 0, speed decreases. If v <= 0 speed increases. 16

Physics 101: Lecture 5, Pg 6 Free Fall ACTS Fred throws a ball 30 mph vertically upward. Which of the following statements are true about the ball’s velocity and acceleration. (Let up be the positive direction) 20 On the way up? On the way down? A) v 0 A) a 0 A) v 0 A) a 0

Physics 101: Lecture 5, Pg 7 ACT Fred throws a ball 30 mph vertically upward and then catches it again at the same height he threw it from. What is the speed of the ball when he catches it? (Neglect air resistance) 1) v 30 mph  v y 2 = v y g(y-y 0 )  v y 2 = v y0 2 23

Physics 101: Lecture 5, Pg 8 Free Fall Example Fred throws a ball 30 m/s vertically upward. What is the maximum height the ball reaches? How long does it take to reach this height? v 2 -v o 2 = 2 a  y  y = (v 2 -v o 2 )/ (2 a) = / (2 * -9.8) = 46 m. 30 v = v 0 + a t t = (v-v 0 ) / a = (0 – 30 m/s )/ (-9.8 m/s 2 ) = 3.1 seconds

Physics 101: Lecture 5, Pg 9 Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball hits the ground first? A. Dennis' ball B. Carmen's ball C. Same v0v0v0v0 v0v0v0v0 Dennis Carmen H vAvAvAvA vBvBvBvB ACT y = y o +v o t + ½ a t 2 32 Dennis: 0 = H + v o t - ½ g t 2 Carmen: 0 = H - v o t - ½ g t 2

Physics 101: Lecture 5, Pg 10 Dennis and Carmen are standing on the edge of a cliff. Dennis throws a basketball vertically upward, and at the same time Carmen throws a basketball vertically downward with the same initial speed. You are standing below the cliff observing this strange behavior. Whose ball is moving fastest when it hits the ground? A. Dennis' ball B. Carmen's ball C. Same v0v0v0v0 v0v0v0v0 Dennis Carmen H vAvAvAvA vBvBvBvB ACT Correct : v 2 = v g  y 35

Physics 101: Lecture 5, Pg 11 Apparent Weight Recall:  F = m a è Consider person accelerating up in an elevator. è Draw FBD è Apply NSL »N – mg = ma »N = m(g+a) mg N y x Apparent weight is normal force from scale or floor. Note: in free fall a=-g so N=0 33

Physics 101: Lecture 5, Pg 12 Apparent Weight Preflight l You are traveling up on an elevator to the 30 th floor of the Sears tower. As it nears the 30 th floor, your weight appears to be 1) heavier 2) the same 3) lighter  F y = ma y N – mg = ma y N = m(g+a) a < 0. so N < mg 40 mg N 50% 20% 30% “When approaching your destination the elevator begins to decelerate, which reduces the apparent weight”

Physics 101: Lecture 5, Pg 13 Great Explanations! (Wrong Answer) “My man Newton put it nicely, an object at rest stays at rest, and an object moving stays moving. You are the object, you are at rest. When the elevator pushes you up, your body ‘stays’ there, it doesn’t want to move. Then, the gravitational force pulls you down, resulting in the increase in mass.” “Your weight remains unchanged as you approach the top of the Sears Tower because as long as you are moving at constant velocity your weight would remain unchanged. However, as soon as you speed up or slow down, the scale would show a different weight.”

Physics 101: Lecture 5, Pg 14 Apparent Weight Acts l A person has mass 50 kg. What is their apparent weight when they are riding on an elevator 1. Going up with constant speed 9.8 m/s 2. Going down with constant speed 9.8 m/s 3. Accelerating up at a rate of 9.8 m/s 2 4. Accelerating down at a rate of 9.8 m/s 2 45 N = m(g+a) a = 0 so N= mg = 490 Newtons a = +9.8 m/s so N= 2 mg = 980 Newtons a = -9.8 m/s so N= 0 mg = 0 Newtons

Physics 101: Lecture 5, Pg 15 Apparent Weight Example l You are standing on a scale inside an elevator. You weigh 125 pounds, but the scale reads 140 pounds. The elevator is going (up down can’t tell) The elevator is accelerating (up down can’t tell) y x 45 N = m(g+a) Weight increases when accelerating up decreases when accelerating down. 49 A B C

Physics 101: Lecture 5, Pg 16 Summary of Concepts l Free Fall è Only force is gravity è Acceleration if 9.8 m/s 2 down l Apparent Weight (Normal Force) è If object is accelerating in vertical direction weight appears different è Accelerating up, increases apparent weight è Accelerating down decreases apparent weight 50