Welcome back to Physics 211 Today s agenda: Forces in Circular Motion Impulse Physics 211 Spring 2014 Lecture 07-1 1 ask a physicist My question is on sonoluminescence, which is supposed to be when a sound wave hits an air bubble underwater, and it's reaction is that it creates light. Is there any truth to this? How does that happen? Physics 211 Spring 2014 Lecture 07-1 2 1
sonoluminescence http://www.youtube.com/watch? v=gjolilubdnw Light emitted from collapsing bubbles in a liquid under sound pressure inertia of water! Temperatures of about 10,000 K 2 to 4 times that of the sun Pistol shrimp Physics 211 Spring 2014 Lecture 07-1 3 Midterm 2: in a week! (3/4) In Stolkin (here!) at the usual lecture time Material covered: Textbook chapters 5-8 (and 1-4) Lectures up through 2/24 (Today -- slides online) Wed/Fri recitation activities Homework assignments You will be given a formula sheet at the exam. A copy of this sheet is available on the course website You should bring a calculator, but you must bring your own, and it can not be a phone. You may not store any equations in memory, and midterm proctors may request to see your calculator during the exam. Exam accommodations: must take exam at ODS Physics 211 Spring 2014 Lecture 07-1 4 2
Forces in circular motion Motion around circular track, constant speed (for now): a rad = v 2 /r Physics 211 Spring 2014 Lecture 07-1 5 A ball is rolling counter-clockwise at constant speed on a circular track. One quarter of the track is removed. What path will the ball follow after reaching the end of the track? Physics 211 Spring 2014 Lecture 07-1 6 3
QuickCheck 8.3 7-1.1 An ice hockey puck is tied by a string to a stake in the ice. The puck is then swung in a circle. What force or forces does the puck feel? 1. A new force: the centripetal force. 2. A new force: the centrifugal force. 3. One or more of our familiar forces pushing outward. 4. One or more of our familiar forces pulling inward. 5. I have no clue. Physics 211 Spring 2014 Lecture 07-1 7 Slide 8-44 QuickCheck 8.4 7-1.2 An ice hockey puck is tied by a string to a stake in the ice. The puck is then swung in a circle. What force is producing the centripetal acceleration of the puck? 1. Gravity 2. Air resistance 3. Friction 4. Normal force 5. Tension in the string Physics 211 Spring 2014 Lecture 07-1 8 Slide 8-46 4
QuickCheck 8.7 7-1.3 A coin sits on a turntable as the table steadily rotates ccw. What force or forces act in the plane of the turntable? Physics 211 Spring 2014 Lecture 07-1 9 Slide 8-68 7-1.4 A car turns a corner on a banked road. Which of the diagrams could be the car s free-body diagram? Physics 211 Spring 2014 Lecture 07-1 10 Slide 8-56 5
Sample problem: A 1000 kg car is going around a banked, frictionless circular track with radius 100 m and and bank angle of 10 degrees. How fast should the car go so that it doesn t slide off the track? car θ W N R Physics 211 Spring 2014 Lecture 07-1 11 7-1.5 A roller coaster car does a loop-the-loop. Which of the free-body diagrams shows the forces on the car at the top of the loop? Rolling friction can be neglected. Physics 211 Spring 2014 Lecture 07-1 12 Slide 8-82 6
Motion on loop-the-loop What is normal force on car at top and bottom of loop? Neglect friction; assume moves with speed v B at bottom and v T at top car At bottom At top Physics 211 Spring 2014 Lecture 07-1 13 Demo swinging water bucket Does the water fall out? What is the FBD for the water? Physics 211 Spring 2014 Lecture 07-1 14 7
Demo swinging water bucket So why doesn t the water fall out? What if mv 2 /R < mg for the water? This is like a satellite in orbit around the earth Physics 211 Spring 2014 Lecture 07-1 15 7-1.6 A physics textbook swings back and forth as a pendulum. Which is the correct free-body diagram when the book is at the bottom and moving to the right? Physics 211 Spring 2014 Lecture 07-1 16 Slide 8-78 8
Forces in circular motion summary: Draw a free body diagram Sum the forces as usual There IS NOT AN EXTRA centripetal force find F NET (radial) and F NET (other) Velocity is NOT a force THEN figure out what F NET (radial) has to be: in uniform circular motion F NET (radial) = ma a = v 2 /r Physics 211 Spring 2014 Lecture 07-1 17 Impulse Constant force F 12 acting on object 1 due to object 2 for a time Δt yields an impulse I 12 = F 12 Δt In general, for a time varying force need to use this for small Δt and add: I = Σ F(t) Δt = Physics 211 Spring 2014 Lecture 07-1 18 9
Impulse for time varying forces F(t) * area under curve equals impulse t 1 t 2 t Physics 211 Spring 2014 Lecture 07-1 19 Impulse à change in momentum Consider first constant forces... Constant acceleration equation: v f = v i + at mv f - mv i = mat = If we call p = mv momentum we see that Δp = Physics 211 Spring 2014 Lecture 07-1 20 10
Definitions of impulse and momentum Impulse imparted to object 1 by object 2: I 12 = F 12 Δt Momentum of an object: p = mv Physics 211 Spring 2014 Lecture 07-1 21 Impulse-momentum theorem I net = Δp The net impulse imparted to an object is equal to its change in its momentum. Physics 211 Spring 2014 Lecture 07-1 22 11
7-1.7 Consider the change in momentum in these three cases: A. A ball moving with speed v is brought to rest. B. The same ball is projected from rest so that it moves with speed v. C. The same ball moving with speed v is brought to rest and immediately projected backward with speed v. In which case(s) does the ball undergo the largest change in momentum? 1. Case A. 2. Case B. 3. Case C. 4. Cases A and B. Physics 211 Spring 2014 Lecture 07-1 23 Notice By Newton s 3 rd law, the force on the ball is equal and opposite to the force on the student Acts for same time interval à equal and opposite changes in momentum Physics 211 Spring 2014 Lecture 07-1 24 12
Newton s 3rd law and changes in momentum If all external forces (weight, normal, etc.) cancel: Physics 211 Spring 2014 Lecture 07-1 25 Conservation of momentum Assuming no net forces act on bodies there is no net impulse on composite system Therefore, no change in total momentum Δ(p 1 + p 2 ) = 0 F 1 2 system Physics 211 Spring 2014 Lecture 07-1 26 13
Conservation of momentum (for a system consisting of two objects 1 and 2) Δp 1 = Δp 2 If the net (external) force on a system is zero, the total momentum of the system is constant. Whenever two or more objects in an isolated system interact, the total momentum of the system remains constant Physics 211 Spring 2014 Lecture 07-1 27 Conservation of momentum with carts One cart with mass m 1 begins at rest v 1i = 0, and the other cart (with the same mass) has a velocity v 2i = v. After the two carts hit each other, what is the sum of the velocities of the two carts v 2f + v 1f? Physics 211 Spring 2014 Lecture 07-1 28 14