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Ph sics 131: Physics 131 Re Review ie Agenda for Today Review Ch 99-12 and 14 Physics 201: Lecture 1, Pg 1 Impulse-Momentum Theorem An impulse on an object leads to a change in the objects momentum. (This is a vector) J x p x J x pfx pix pfx pix J x The momentum ‘after’ an interaction, like a collision or explosion, equals the momentum before the interaction plus the impulse that arises from the interaction. Physics 201: Lecture 1, Pg 2 Clicker Question 1: You drop an egg onto A) the floor B) a thick piece of foam rubber rubber. In both cases cases, the egg does not bounce (Assume the egg hits each surface with the same speed). I which In hi h case iis th the magnitude it d off the th average force f greater? t ? A) Floor B) Foam C) It’s the same Pre-class Quiz: This is why cars have crumple zones, to increase t and decrease the force. J y mv Favg y t mv mv Favg y t Physics 201: Lecture 1, Pg 3 Conservation of Momentum Newton’s Newton s second law for a system ext Fnet dp dt The total momentum of an isolated system remains constant Isolated system y = no external forces Physics 201: Lecture 1, Pg 4 Clicker Question 2: A mosquito and a truck have a head-on collision. Which h a llarger change has h off momentum? t ? A. The mosquito. B. The truck. C. They have the same change of momentum. D. Can Can’tt say without knowing their initial velocities. Physics 201: Lecture 1, Pg 5 Clicker Question 2.5: Two blocks of masses m and 2m are placed in contact on a horizontal, frictionless surface, with the more massive block on the left. A force of magnitude F = 10.0 N, pointing to the right, is applied to the more massive block for a time of 5.00 s. What is the net impulse imparted to the more massive block? (A) (B) (C) (D) (E) 11.2 N-s 16.7 N-s 33 33.3 3N N-ss 50.0 N-s 25.0 25 0 N-s Ns Physics 201: Lecture 1, Pg 6 Clicker Question 2.5: Two blocks of masses m and 2m are placed in contact on a horizontal, frictionless surface, with the more massive block on the left. A force of magnitude F = 10.0 N, pointing to the right, is applied to the more massive block for a time of 5 5.00 00 ss. What is the net impulse imparted to the more massive block? Physics 201: Lecture 1, Pg 7 Energy is Conserved Energy is “Conserved” Conserved meaning it can not be created nor destroyed g form Can change Can be transferred Total Energy does not change with time. This is a BIG deal! Physics 201: Lecture 1, Pg 8 Collisions Momentum is almost always conserved during as collision (external forces are generally small compared to collision forces) T Two kinds ki d off collisions lli i Elastic-KE is conserved Very special case Inelastic-KE is not conserved Can be assumed if Objects stick together Damage is done during collision Physics 201: Lecture 1, Pg 9 Elastic Collision During D i an elastic l ti collision lli i b both th momentum t and d mechanical energy are conserved: m1v1f m2 v2 f m1 v1i m2 v2 i 1 2 (1) m1v1f m2 v 2 f m1 v1i m2 v 2 i 2 1 2 2 1 2 2 1 2 2 (2) Combining equation (1) and (2) we get that “speed of approach equals speed of recession”: v2 f v1f v2 i v1i Together with equation (1) you can solve for just about any 1 d elastic collision 1-d Physics 201: Lecture 1, Pg 10 Clicker Question 3: There are two identical carts (with the same mass) on a frictionless straight horizontal track. Cart B is initially stationary stationary, and cart A collides into cart B. B Can A reverse its direction of motion after the collision? (A) No, never. (B) Yes Yes. (C) It depends on the details of the collision. Physics 201: Lecture 1, Pg 11 Problem A ball of clay of mass m = 0.2 0 2 kg strikes a block of mass M = 8.0 kg which slides on a frictionless table as it compresses a spring with spring constant k = 60 N/m. The initial speed of the ball of clay is v = 12 m/s m/s. The spring is initially at its relaxed length. What is the maximum compression of the spring, d, after the collision (the clay sticks to the block)? Vafter collision = 0.29 m/s x = 0.108 m Physics 201: Lecture 1, Pg 12 Problem A ball of clay of mass m = 0.2 0 2 kg strikes a block of mass M = 8.0 kg which slides on a frictionless table as it compresses a spring with spring constant k = 60 N/m. The initial speed of the ball of clay is v = 12 m/s m/s. The spring is initially at its relaxed length. What is the maximum compression of the spring, d, after the collision (the clay sticks to the block)? Vafter collision = 0.29 m/s x = 0.108 m Physics 201: Lecture 1, Pg 13 Clicker Question 4: A pendulum consists of a mass m = 0.2 kg on the end of a string of length L = 0 0.3 3m m. At the moment the mass at its lowest point, it is observed that the speed of the mass is v = 2.2 m/s. What can we say about the work Ws done by the string? A. Ws > 0 B. Ws < 0 C. Ws = 0 Physics 201: Lecture 1, Pg 14 The Work-Energy Theorem Wtot = ½mvf2 - ½mvi2 Put positive work into an object, its speed increases! Put negative work into an object, its speed decreases! Be careful, we are interested in total work done!!! We W mustt look l k att all ll forces f acting, ti nott just j t one!! Physics 201: Lecture 1, Pg 15 Clicker Question 5: Suppose a cable pulls an elevator of mass M up a height h at constant speed v. v What is the net work done (sum of the work done by all external forces) on the elevator as it moves up this height h? (A) (B) (C) (D) (E) Mgh 0 (1/2) M v2 -Mgh - (1/2) M v2 Physics 201: Lecture 1, Pg 16 The Work-Energy Theorem Wtot = K WC + WNC = K WNC = K – WC WNC = K + U Physics 201: Lecture 1, Pg 17 Conservation of Mechanical Energy G d when Good h only l gravity it or a spring-like i lik force f are doing d i work on an object Emech f = Emech i Kf + Uf = Ki + Ui ½ksf2 + ½mv ½k ½ f2 + mgh hf = ½ks ½k i2 + ½mv ½ i2 + mgh hi Physics 201: Lecture 1, Pg 18 Clicker Question 6: Ball A is dropped from rest from a window. At the same instant, ball B is thrown downward; and ball C is thrown upward from the same window. Which statement concerning the balls is necessarily true if air resistance is neglected? A. At some instant after it is thrown, the acceleration of ball C is zero B. All three balls reach the ground with the same velocity C. All three balls strike the ground at the same time D All three balls have the same acceleration at any D. instant E. All three balls have the same velocityy at anyy instant Physics 201: Lecture 1, Pg 19 Two cases First case: Point mass objects An object that is so small compared with its distance from the axis we can forget about its size i and d consider id allll off iits mass acting i at one point = mr2 Second case: common objects around common rotation axes Textbook pg 318 Physics 201: Lecture 1, Pg 20 Clicker Question 7: Which dumbbell has the larger moment of inertia about the midpoint of the rod? The connecting rod is massless. A. Dumbbell A. B Dumbbell B. D bb ll B B. C. Their moments of inertia are the same. Physics 201: Lecture 1, Pg 21 Newton’s second law in rotation land Sum of the torques will equal the moment of inertia times the angular acceleration = An unbalanced net torque will result in an angular acceleration Physics 201: Lecture 1, Pg 22 Clicker Question 8: Which third force on the wheel, applied at point P, will make the net torque zero? Physics 201: Lecture 1, Pg 23 Positive vs. Negative torque Torque can be positive or negative Call counterclockwise positive rotation Positive rotation F1 F2 F1 wants to rotate negative; F2 positive Physics 201: Lecture 1, Pg 24 Static Equilibrium An object is in static equilibrium if all the forces and torques acting on it sum to zero FX = 0 and d FY = 0 As well We will learn to apply these laws to problems and solve for various unknowns = 0 Physics 201: Lecture 1, Pg 25 Clicker Question 9: Which object is in static equilibrium? Physics 201: Lecture 1, Pg 26 Clicker Question 10: A 1-kg ball is hung at the end of a rod 1-m long. g If the system y balances at a p point on the rod 0.25 m from the end holding the mass, what is the mass of the rod? a) ¼ kg b) ½ kg 1m c) 1 kg d) 2 kg 1kg e) 4 kg Physics 201: Lecture 1, Pg 27 Clicker Question 10: 1m 1kg Physics 201: Lecture 1, Pg 28 Clicker Question 11: A uniform p plank ball has a mass 2M and a bowling g ball has a mass M. The length of the plank is 5m and it rests horizontally on two supports, as shown in the drawing, with 2m of the p plank hanging g g over the right g support. pp To what distance xtip (measured from the right-most support) can the bowling ball be rolled onto the overhanging part of the plank before the plank just begins to tip? (a) xtipp = 0.3 m (b) xtip = 0.5 05m (c) xtip = 0.7 m (d) xtipp = 0.8 m (e) xtip = 1.0 m Physics 201: Lecture 1, Pg 29 Clicker Question 11: Physics 201: Lecture 1, Pg 30 Linear and Angular g Linear Displacement s Velocity y v Acceleration a Inertia m K ½ m v2 N2L F = ma Momentum p = mv Angular I ½ I 2 = I L = Iw Physics 201: Lecture 1, Pg 31 Conservation of Angular Momentum Newton’s Newton s second law for rotations L ext t The angular momentum of an isolated system is conserved Physics 201: Lecture 1, Pg 32 Clicker Question 12: You are holding a spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning in the opposite direction, the turntable will: a) remain stationary b) start to spin in the same direction as before flipping c) to spin in the same direction as after flipping Physics 201: Lecture 1, Pg 33 Clicker Question 13: You want to measure the moment of inertia for a rotating oval object. Initially, this object has an angular speed of 35 rad/s. You drop a ring of mass 30 kg and radius 0 0.2 2 m on top of the object. The ring and object apply frictional forces on each other and eventually come to have the same angular speed of 24 rad/s. What is the moment of inertia of the object? (a) 4.67 kg m2 ( ) 2.62 kg m2 (b) (c) 3.45 kg m2 ((d)) 8.92 kg g m2 i 2 (e) 1.23 kg m initial ring f final Physics 201: Lecture 1, Pg 34 Clicker Question 14: A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around itit, and weight is hanging on the string with m = 4.1 kg. The system of the weight and disk is released from rest. When the 4.1 kg weight is moving with a speed of 1 1.5 5 m/s m/s, what is the angular speed of the disc? (a) (b) (c) (d) (e) 0.375 rad/s 0.5 rad/s 1.5 rad/s 6 rad/s 8 rad/s Physics 201: Lecture 1, Pg 35 Clicker Question 15: A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around itit, and weight is hanging on the string with m = 4.1 kg. The system of the weight and disk is released from rest. When the 4.1 kg weight is moving with a speed of 1 1.5 5 m/s m/s, what is the kinetic energy of the entire system? (a) (b) ( ) (c) (d) (e) 13 J 4.6 J 7.8 8J 15 J 9 9.2 2J Physics 201: Lecture 1, Pg 36 Clicker Question 16: A 15 kg g uniform disk of radius R = 0.25 m has a string g wrapped around it, and weight is hanging on the string with m = 4.1 kg. The system of the weight and disk is released from rest. When the 4.1 kg g weight g is moving g with a speed of 1.5 m/s, what is the kinetic energy of the entire system? Physics 201: Lecture 1, Pg 37 Clicker Question 17: A 15 kg uniform disk of radius R = 0.25 m has a string wrapped around itit, and weight is hanging on the string with m = 4.1 kg. The system of the weight and disk is released from rest. When the 4.1 kg weight is moving with a speed of 1 1.5 5 m/s m/s. If the system started at rest rest, how far has the weight fallen in this time? (a) 1.2 m (b) 0.5 m (c) 0.3 m (d) 0 0.9 9m (e) 3.17 m Physics 201: Lecture 1, Pg 38 Clicker Question 18: An 0.80 kg object is attached to one end of a spring, and the system is set into simple harmonic motion motion. The displacement of x of the object as a function of time is shown in the drawing. What is the angular frequency ? (a) (b) (c) (d) (e) 4 rad/s 0 0.25 25 rad/s 1.57 rad/s 15 5 rad/s ad/s 2.2 rad/s What is the frequency f? Physics 201: Lecture 1, Pg 39 Clicker Question 19: An 0.80 kg object is attached to one end of a spring, and the system is set into simple harmonic motion motion. The displacement of x of the object as a function of time is shown in the drawing. What is the magnitude of the speed of the object at t = 2 s? ( ) (a) (b) (c) (d) (e) 0.4 m/s 0 m/s 0.13 m/s 0.78 m/s 2.0 m/s Physics 201: Lecture 1, Pg 40 Clicker Question 20: An 0.80 kg object is attached to one end of a spring, and the system is set into simple harmonic motion motion. The displacement of x of the object as a function of time is shown in the drawing. What is the magnitude of the acceleration of the object at t = 1 s? ( ) (a) (b) (c) (d) (e) 4 m/s2 0 m/s2 1.64 m/s2 0.20 m/s2 2.0 m/s2 Physics 201: Lecture 1, Pg 41 Clicker Question 21: An 0.80 kg object is attached to one end of a spring, and the system is set into simple harmonic motion motion. The displacement of x of the object as a function of time is shown in the drawing. What is the spring constant k? (a) (b) (c) (d) (e) 4 N/m 0.25 0 25 N/m 1.28 N/m 0 0.78 8 N/m / 2.0 N/m Physics 201: Lecture 1, Pg 42