Page 1Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 1"Professor Goddard does not know the relation between action andreaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." New York Times editorial, 1921, about Robert Goddard's revolutionary rocket work."Correction: It is now definitely established that a rocket can function in a vacuum. The 'Times' regrets the error." New York Times editorial, July 1969.Lecture 7Physics 207: Lecture 7, Pg 2Lecture 7Goals:Goals: Solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1stand 2ndlaws. Distinguish static and kinetic coefficients of friction Differentiate between Newton’s 1st, 2ndand 3rd LawsAssignment: HW4, (Chapters 6 & 7, due 2/18, 9 am, Wednesday)Read Chapter 7 1stExam Wednesday, Feb. 18 from 7:15-8:45 PM Chapters 1-7Page 2Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 3Exercise, Newton’s 2ndLawA. P + C < WB. P + C > WC. P = CD. P + C = WA woman is strainingto lifta large crate,withoutsuccess. Itistooheavy. We denotetheforces onthe crate asfollows:P is the upward force being exerted on the crate by the personC is the contact or normal force on the crate by the floor, and W is the weight (force of the earth on the crate). Whichof followingrelationships betweentheseforces istrue,whilethe person istrying unsuccessfullyto lift thecrate? (Note:force up is positive & down is negative)Physics 207: Lecture 7, Pg 4Mass We have an idea of what mass is from everyday life. In physics: Mass (in Phys 207) is a quantity that specifies how much inertia an object has (i.e. a scalar that relates force to acceleration)(Newton’s Second Law) Mass is an inherent property of an object. Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force. “Pound” (lb) is a definition of weight (i.e., a force), not a mass!Page 3Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 5Inertia and Mass The tendency of an object to resist any attempt to change its velocity is called Inertia Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity (acceleration)If mass is constant thenIf force constant Mass is an inherent property of an object Mass is independent of the object’s surroundings Mass is independent of the method used to measure it Mass is a scalar quantity The SI unit of mass is kgnetFarr∝ma1||∝r|a|mPhysics 207: Lecture 7, Pg 6ExerciseNewton’s 2ndLawA. increasingB. decreasingC. constant in timeD. Not enough information to decide An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time(read this text carefully). The speed of the object isPage 4Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 7Exercise Newton’s 2ndLawA. BB. CC. DD. FE. GA 10 kg mass undergoes motion along a line with a velocities as given in the figure below. In regards to the stated letters for each region, in which is the magnitude of the force on the mass at its greatest?Physics 207: Lecture 7, Pg 8Home ExerciseNewton’s 2ndLawA. 4 x as longB. 2 x as longC. 1/2 as long D. 1/4 as longA constant force is exerted on a cart that is initially at rest on an air table. The force acts for a short period of time and gives the cart a certain final speed s.Air TrackCartForceIn a second trial, we apply a force only half as large.To reach the same final speed, how long must the same force be applied (recall acceleration is proportional to force if mass fixed)?Page 5Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 9Home Exercise Newton’s 2ndLawSolutionAir TrackCartForce(B) 2 x as longF = maSince F2= 1/2 F1a2= 1/2 a1We know that under constant acceleration, v = a ∆tSo,a2∆t2= a1∆t1 we want equal final velocities1/2 a1/ ∆t2= a1/ ∆t1∆t2= 2 ∆t1Physics 207: Lecture 7, Pg 10Home ExerciseNewton’s 2ndLawA. 8 x as far B. 4 x as far C. 2 x as far D. 1/4 x as far A force of 2 Newtons acts on a cart that is initially at reston an air track with no air and pushed for 1 second. Because there is friction (no air), the cart stops immediately after I finish pushing. It has traveled a distance, D. Air TrackCartForceNext, the force of 2 Newtons acts again but is applied for 2 seconds. The new distance the cart moves relative to D is:Page 6Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 11Home ExerciseSolutionAir TrackCartForce(B) 4 x as longWe know that under constant acceleration, ∆x = a (∆t)2 /2 (when v0=0)Here ∆t2=2∆t1, F2= F1⇒ a2= a1( )4221212121212212=∆∆=∆∆=∆∆tttataxxPhysics 207: Lecture 7, Pg 12Home Exercise: Physics in an ElevatorGravity and Normal ForcesA woman in an elevator is accelerating upwardsThe normal force exerted by the elevator on the woman is,(A) greater than(B) the same as(C) less thanthe force due to gravity acting on the woman(REMEMBER: Draw a FREE BODY DIAGRAM)Page 7Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 13Moving forces around Massless strings: Translate forces and reverse their direction but do not change their magnitude(we really need Newton’s 3rdof action/reaction to justify) Massless, frictionless pulleys: Reorient force direction but do not change their magnitudestringT1-T1T1-T1T2-T2| T1 | = | -T1 | = | T2 | = | T2 | Physics 207: Lecture 7, Pg 14Scale Problem You are given a 1.0 kg mass and you hang it directly on a fish scale and it reads 10 N (g is 10 m/s2). Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale. What force does the fish scale now read?1.0 kg10 N?1.0 kgPage 8Physics 207 – Lecture 7Physics 207: Lecture 7, Pg 15Scale Problem Step 1: Identify the system(s). In this case it is probably best to treat each object as a distinct element and draw three force body diagrams. One around the scale One around the massless pulley (even though massless we can treat is as an “object”) One around the hanging mass Step 2: Draw the three FBGs. (Because this is a now a one-dimensional problem we need only consider forces in the y-direction.)?1.0 kgPhysics 207: Lecture 7,
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