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UW-Madison PHYSICS 107 - PHYSICS 107 Exam 1

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Sep. 27, 2004 Physics 107, Lecture 10Exam #1• Hour Exam I, Wednesday Sep 29, in-class• Material from Chapters 1,3,4,5,6• One page of notes (8.5” x 11”) allowed.Can write on both sides• Questions are multiple choice• Scantron sheets will be used -bring #2 HB pencils and calculatorOn-line review questions for chapters 3-6 atuw.physics.wisc.edu/~rzchowski/phy107Sep. 27, 2004 Physics 107, Lecture 10Chapter 1• How science is done.• Experience and reason• Theory should describe the physical world.• Often required to accept unusual ideas in order toexplain experiments.• Examples of geocentric theories replaced byheliocentric based on– Fit to more accurate experimental data.– Unwieldy nature of heliocentric theories.Sep. 27, 2004 Physics 107, Lecture 10Chapter 3: Post-Aristotle• Inertia:A body subject to no external forces will– Stay at rest if it began at rest– Will continue motion in straight line atunchanging speed if it began in motion.• Can explain how moon keeps orbiting aroundearth, etc.• But need details to quantify thisSep. 27, 2004 Physics 107, Lecture 10Chapter 3: more definitions € Average speed = distance traveledtraveling timeAs an equation: € Distance traveled = dTraveling time = tAverage speed = s € s =dt € Acceleration is the rate at which velocity changes :Acceleration = change in velocitytime to make the changeInstantaneous speed and accel = average valuesover short time interval.Sep. 27, 2004 Physics 107, Lecture 10Example of falling ball00.511.522.530 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Falling BallDISTANCE ( meters )TIME ( seconds ) € speed =0.4m − 0.2m0.275s − 0.18s= 2.1m / s0.22s € speed =1.2m − 0.8m0.488s − 0.40s= 4.5m / s0.45s € speed =2.6m − 2.0m0.73s − 0.638s= 6.5m / s0.69sSep. 27, 2004 Physics 107, Lecture 10Falling ball: constant accel.• Instantaneous speedincreases proportionallyto time for falling ball• s=ata=9.81 m/s2 =acceleration of gravity012345670 0.1 0.2 0.3 0.4 0.5 0.6 0.7VELOCITY ( m/s)TIME ( s )€ d =12at2For constant accel:Sep. 27, 2004 Physics 107, Lecture 10QuestionA car has a constant acceleration of 10 km/hr/s. Howlong will it take to accelerate to 100 km/hr?A. 5 secondsB. 10 seconds.C. 12 seconds.Each second, the velocity increases by 10 km/hr.Starting from zero, it would take 10 seconds toreach 100 km/hr.Sep. 27, 2004 Physics 107, Lecture 10Chapter 4• Principle of inertia:– object continues in its state of rest, or uniform motion in astraight line, unless acted upon by a force.• Defined mass m:– amount of inertia of a body– Measured in kg• Define force F:– Something that changes a body’s acceleration• Related force, mass, and acceleration:– F=ma, or a=F/m– Subject to the same force,more massive objects accelerate more slowly.• Weight:– Force of gravity on a body = mg– Measured in newtons (N). 1 N = 1 kg-m/s2Sep. 27, 2004 Physics 107, Lecture 10QuestionA 1 kg object, weighing 10 N on Earth,is moved to outer space.A. It’s mass is zero and it’s weight is zero.B. It’s mass is 1 kg and it’s weight is zero.C. It’s mass is zero and it’s weight is 10 N.Mass is an intrinsic characteristic of a body.The force of gravity on the body (weight) willdepend on the other bodies around it.Sep. 27, 2004 Physics 107, Lecture 10Chapter 4: Newton• Net Force = Mass x Acceleration € Acceleration =Net ForceMass€ a =Fm•Constant force gives constant accel:Velocity increases with time.Sep. 27, 2004 Physics 107, Lecture 10Chap. 4: Law of force pairs• Every force is an interaction between two objects• Each of the bodies exerts a force on the other.• The forces are equal and opposite– An action-reaction pair.Force on theblock by youForce by theblock on youand the earth!Sep. 27, 2004 Physics 107, Lecture 10QuestionTwo people are on roller chairs, and quickly pushoff of each other as hard as they can. Theyhave masses of 100 kg and 50 kg. After thepush, the 100 kg person is movingA. Twice as fast as the 50 kg personB. The same speed as the 50 kg personC. Half as fast as the 50 kg personEqual and opposite forces, but a=F/m, sothe accel of 100 kg person is half that of50 kg person. Accel is applied for sametime, and v=atSep. 27, 2004 Physics 107, Lecture 10Newton’s laws of motion1) Every object continues in its state of rest, oruniform motion in a straight line, unless actedupon by a force.2) The acceleration of a body along a direction isproportional to the total force along that direction, andinversely proporational to the mass of the body.3) The forces exerted between two interacting objectsare equal in magnitude and opposite in direction.F=ma or, a = F/mSep. 27, 2004 Physics 107, Lecture 10Some equations• Constant speed (no forces)– distance=(velocity)x(time), d=vt– v=constant• Constant accel (constant force)– d=(1/2)x(accel)x(time)2, d=(1/2)at2– v=at,– a=constantSep. 27, 2004 Physics 107, Lecture 10QuestionYou measure the depth of a well by dropping arock, and measuring the time until the splash.You measure 2 seconds. The well is…A. 10 mB. 20 mC. 40 m€ d =12at2=12(10m /s2) × (2s)2= 20mSep. 27, 2004 Physics 107, Lecture 10Chapter 5• Centripetal acceleration: body in circularorbit at constant speed has an accelerationdirectly inward.– magnitude is v2/r. r=orbital radius• Gravitational force:– Force between any two bodies with mass– F= GM1M2/r2– r = separation between centers• Free-fall– Accelerating at acceleration of gravitySep. 27, 2004 Physics 107, Lecture 10Acceleration = € change in velocitychange in timeVelocity at time t1Velocity at time t2•Speed is same, but direction haschanged•Velocity has changed•Centripetal accel = v2/rV(t1)V(t2)Change in velocitySep. 27, 2004 Physics 107, Lecture 10Properties of gravity• Gravitational force between two objectsproportional to product of masses• Gravitational force drops with the square ofthe distance between centers of objects.Sep. 27, 2004 Physics 107, Lecture 10Equation for force of gravity € Fgravity∝(Mass of object 1)×(Mass of object 2)square of distance between them € F ∝m1× m2d2 € F = 6.7 ×10-11m1× m2d2For masses in kilograms, and distance in meters,Sep. 27, 2004 Physics 107, Lecture 10Chaotic motion• Chaotic systems:– Exactly follow Newton’s laws of motion (deterministic)– Sensitive dependence on initial conditions– Details of this dependence can show fractal (self-similar) behavior.–


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UW-Madison PHYSICS 107 - PHYSICS 107 Exam 1

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