Purdue University, Physics 220 Lecture 04 Forces and Motion in 1 D Textbook Sections 3.2-3.6 Lecture 4 Purdue University, Physics 220

Graphing calculator are not allowed during exams. Because they it can store nearly everything in memory. Lecture 3 Purdue University, Physics 220

Purdue University, Physics 220 Mass and Weight Mass: quantifies the amount of inertia that an object possesses – an intrinsic property of the object Weight (Gravitational force exerted by the Earth) W = mg (g-acceleration due to gravity) g = GMearth/(rearth)2 = 9.8 m/s2 (G – universal gravitational constant, more in Chapter 5) Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Contact Forces Normal force: a contact force acting at an interface perpendicular to the surface of contact Frictional force: another contact force acting at an interface parallel to the surface of contact resist motion of the two surfaces sliding past each other always act opposite the direction of motion mg N F Ff Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Friction Magnitude of frictional force is proportional to the normal force. Fkinetic = mk N mk coefficient of kinetic friction Fstatic  ms N ms coefficient of static friction Be Careful! Static friction , can be any value up to msN Direction always opposes motion Lecture 4 Purdue University, Physics 220

Friction and Walking The person “pushes” off during each step The bottoms of his shoes exert a force on the ground If the shoes do not slip, this force is due to static friction The shoes do not move relative to the ground

Book Pushed Across Table Book sliding across table Isolate the object of interest (book) Identify all forces acting on the object Hand (to right) Gravity (down) Normal (table, up) Friction (table, left) Choose a coordinate system y x Normal friction hand Gravity Physics Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Contact Force: Spring Force exerted by a spring is directly proportional to the amount by which it is stretched or compressed. Fspring = k x always trying to restore its original length Example: When a 5 kg mass is suspended from a spring, the spring stretches 8 cm. Determine the spring constant. Fspring Fspring- Fgravity = 0 Fspring = Fgravity k x = m g k = m g / x = (5 kg) x (9.8 m/s2) /(0.08 m) = 612 N/m Maybe simple demo, add twice as much mass, get twice the stretching before showing the slide. Also make note that this is NOT as big a deal as Newton’s laws. Just an example of a contact force. Fgravity y x Lecture 4 Purdue University, Physics 220

Contact Force: Tension A force transmitted by a rope, cord, cable or the like which transmits a force from one end to an object attached at the other end Ideal string (or cord, rope, etc.): Always maintains constant tension everywhere. Has a zero mass. Tension is parallel to the string Pulley changes the direction of the force associated with the tension in the rope. Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 iClicker Two boxes are connected by a string over a frictionless pulley. In equilibrium, box 2 is lower than box 1. Compare the weight of the two boxes. A) They have the same weight B) Box 1 is heavier C) Box 2 is heavier 1 T m1g 1 SF = 0 1) T - m1 g = 0 2) T – m2 g = 0 => m1 = m2 2 T m2g 2 Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Tension Example Determine the force exerted by the hand to suspend the 45 kg mass as shown in the picture. 1) 220 N 2) 440 N 3) 660 N 4) 880 N 5) 1100 N y x T T SF = 0 T + T – W = 0 2 T = W T = m g / 2 = (45 kg x (9.8 m/s2)/ 2 = 220 N W Remember the magnitude of the tension is the same everywhere along the rope! Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Question What is the force on the ceiling? y x A) 220 N B) 440 N C) 660 N D) 880 N E) 1100 N SF = 0 Fc -T - T – T = 0 Fc = 3 T Fc = 3 x 220 N = 660 N Fc T Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Question What does the scale read? A) 225 N B) 550 N C) 1100 N The sum of the forces here will be 0. Thus, the force tension will equal the force gravity. Since the force of gravity is 550N, the force of tension (which is measured by the scale) will also be 550N. Lecture 4 Purdue University, Physics 220 30

Purdue University, Physics 220 Pulley Example Two boxes are connected by a string over a frictionless pulley. Box 1 has mass 1.5 kg, box 2 has a mass of 2.5 kg. Box 2 starts from rest 0.8 meters above the table, how long does it take to hit the table. Compare the acceleration of boxes 1 and 2 A) |a1| > |a2| B) |a1| = |a2| C) |a1| < |a2| 1) T - m1 g = m1 a1 2) T - m2 g = -m2 a1 using a1 = -a2 2) T = m2 g -m2 a1 1) m2 g -m2 a1 - m1 g = m1 a1 a1 = (m2 – m1)g / (m1+m2) y x 1 Do this on transparency 1 T m1g 2 T m2g 2 Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Pulley Example Two boxes are connected by a string over a frictionless pulley. Box 1 has mass 1.5 kg, box 2 has a mass of 2.5 kg. Box 2 starts from rest 0.8 meters above the table, how long does it take to hit the table. a1 = (m2 – m1)g / (m1+m2) a = 2.45 m/s2 Dx = v0t + ½ a t2 Dx = ½ a t2 t = sqrt(2 Dx/a) t = 0.81 seconds y x 1 Do this on transparency 1 T m1g 2 T m2g 2 Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Free Fall At the earth’s surface freely falling bodies experience a constant acceleration of 9.8 m/s2 There is a choice of axes: 1) Choose positive y up in which case a=g=-9.8 m/s2 2) Choose positive y down in which case a=g=9.8 m/s2 y g=9.8 m/s2 Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Free Fall Only force acting on object is GRAVITY Newton’s 2nd Law Fy = may Force is Weight = mg (near surface of earth) -mg = may ay = -g (- sign tells us it is in –y direction or down) Acceleration is always g downwards Velocity may be positive, zero or negative Position may be positive, zero or negative y x Demos penny and feather. First with air resistance, then without. y = y0 + vy0t - 1/2 gt2 vy = vy0 - gt vy2 = vy02 - 2g(y-y0) Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 Example of Free Fall This is for y0=0 and v0=0 Lecture 4 Purdue University, Physics 220

Purdue University, Physics 220 iClicker 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) A) v = 30 mph B) v < 30 mph C) v > 30 mph vy2 = vy02 - 2g(y-y0) vy2 = vy02 Lecture 4 Purdue University, Physics 220

Two blocks one sliding one hanging A block of mass m1=3kg rests on a frictionless horizontal surface. A second block of mass m2=2kg hangs from an ideal cord of negligible mass who runs over an ideal pulley. Block 2 starts from rest 0.8 meters above the floor, how long does it take to hit the floor? a a a1 = (m2 )g / (m1+m2) a = 3.9 m/s2 y = v0t + ½ a t2= ½ a t2 t = sqrt(2 y/a) t = 0.64 seconds Lecture 4 Purdue University, Physics 220