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PHSX213 class • Class stuff – Another problem solving session on Monday 6:00 PM – 7.15 PM (Malott 1089) – Practice exam available (correct answers on web page) – Homework comments – Midterm Exam • More Newton’s Laws examples incl. friction. • Drag force • Circular Motion Fri. Feb. 11th 1 Homework • HW3W due in class. HW3 due at 6PM today. • HW4 should be posted later today, due next Friday at 6 PM. – The chapter 1-6 problems will be relevant to the mid-term exam. But exclusively concentrating on those, without overall revision, probably not the best preparation. • If there is an error in one of the online homework problems and you are the first to point it out correctly – you will get double points for that question. – This could happen because the parameter values in your question are unphysical. (I usually have checked that those for my question are OK) – It may be more likely though that you have some error … Fri. Feb. 11th 2 Midterm Exam • ( r, t ) = ( Budig 120, Wed. Feb. 16th 8:00 – 9:30 PM ) – We will have some small corner in the balcony of this (huge) room. • Chapters 1-6. • If you cannot make this exam time because of some university authorized activity – you need to let me know asap, and preferably document it with an E-mail. • The majority of the exam will consist of multiple choice questions (5 options) similar to the ones from the practice exam I’ll distribute on Friday. – Questions will be a mix of conceptual and short calculations. – Will contain a brief formula sheet (see practice exam). – Only calculator and pencil allowed in exam. • The remainder will probably consist of 1 or 2 questions a bit like the homeworks which should be answered more in the style of my written homework solutions. Fri. Feb. 11th 3 Check-Point 1 In the figure is the tension in the string greater than, less than, or equal to the weight of block B? A. Greater than B. Less than C. Equal to Fri. Feb. 11th 4 Check-Point 1 In the figure is the tension in the string greater than, less than, or equal to the weight of block B? A. Greater than B. Less than C. Equal to Fri. Feb. 11th Object A will accelerate to the right. Object B will accelerate downwards. Forces acting on object B are the force due to gravity 5 downwards, and tension upwards. Static friction on incline If the block just starts to slide at angle to the horizontal of q, what is the value of the coefficient of static friction ? Demo MC3 Fri. Feb. 11th 6 Another worked example Problem 6.23 When the three blocks are released, they accelerate at 0.5 M 2 m/s . What is the coefficient of kinetic friction between block 2 and the table ? Fri. Feb. 11th 2M 2M M M 7 Reading Quiz A car is traveling along a road. Initially it is traveling normally, then it skids. What kind of friction is relevant to these 2 time periods ? A) Static friction, then kinetic friction. B) Kinetic friction, then static friction. C) Static friction all the time. D) Kinetic friction all the time. Fri. Feb. 11th 8 Reading Quiz A car is traveling along a road. Initially it is traveling normally, then it skids on some oil. (It doesn’t have ABS) What kind of friction is relevant to these 2 time periods ? A) Static friction, then kinetic friction. B) Kinetic friction, then static friction. C) Static friction all the time. D) Kinetic friction all the time. Fri. Feb. 11th 9 Check-Point 3 from last time • Why do raindrops fall with constant speed during the later stages of their descent? • A. The gravitational force is the same for all drops • B. Air resistance just balances the force of gravity • C. The drops all fall from the same height • D. The force of gravity is negligible for objects as small as raindrops • E. Gravity cannot increase the speed of a falling object to more than 9.8m/s Fri. Feb. 11th 10 Drag Force • Basic Idea : – object moving through a fluid (eg. air, water) experiences a drag force, FD – which opposes its motion – Depends on the relative speed, v, of the fluid with respect to the object – In some circumstances, FD ~ v2 . • Can apply reasonably well to air and blunt objects • In general dependence is more complicated. Fri. Feb. 11th 11 Terminal Speed • As an object accelerates from rest (eg. in free-fall in air), the speed increases. • So the drag force increases. FD • Eventually there is no net force to further accelerate the object, and it reaches its terminal speed FG = mg • Net downward force (if ~ v2) • mg – k v2 = m dv/dt • Set dv/dt=0 => vT2 = mg/k • Solve DE, v(t) = vT tanh[gt/vT] FG = mg Fri. Feb. 11th FD FG = mg 12 How fast does it reach its terminal speed ? v/vT Example : rain-drop, vT = 7.0 m/s, R=1.5mm (k = 2.2810-6 kg/m) Plots show v/vT = tanh [gt/vT] = tanh[1.4 t] Fri. Feb. 11th t (s) 13 Does it ever really reach its terminal speed ? • • • • • • • These plots show : log10 (1 – v/vT) versus t (s) So -1 = 90% vT -2 = 99% vT -3 = 99.9% vT Etc So, no it never really does, but for practical purposes it does pretty quickly ! Fri. Feb. 11th 14 Check-Point 3 • If a satellite moves above Earth’s atmosphere in a circular orbit with constant speed, then: • A. its acceleration and velocity are always in the same direction • B. the net force on it is zero • C. its velocity is constant • D. it will fall back to Earth when its fuel is used up • E. its acceleration is toward the Earth Fri. Feb. 11th 15 Uniform Circular Motion • In section 4.7 we saw that an object moving in a circular path at constant speed is accelerating towards the center of the circle • aR = - v2/r ^r v • Centripetal force – F = m aR – F = m v2/r Fri. Feb. 11th aR r 16 Loop-the-Loop demo Demo MJ7 Fri. Feb. 11th 17 Other examples • Car on banked road Fri. Feb. 11th 18 Next time • Energy and work. Chapter 7. • (We’re still basically on track with the syllabus schedule) • So for stuff that hasn’t been “covered” in class, you need to read about it ! Fri. Feb. 11th 19