Week 5. Lecture Quiz 1. Forces of Friction, cont. Forces of Friction. Forces of Friction, final. Static Friction

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1 Lectue Quiz 1 Week 5 Fiction (Chapte 5, section 8) & Cicula Motion (Chapte 6, sections 1-) You hae a machine which can acceleate pucks on fictionless ice. Stating fom est, the puck taels a distance x in time t when foce F is applied. If foce 3F is applied, the distance the puck taels in time t is: A. x B. 1.5x C. 3x D. 4.5x E. 9x Foces of Fiction When an object is in motion on a suface o though a iscous medium, thee will be a esistance to the motion This is due to the inteactions between the object and its enionment This esistance is called the foce of fiction Foces of Fiction, cont. Fiction is popotional to the nomal foce ƒ s µ s n and ƒ k = µ k n μ is the coefficient of fiction These equations elate the magnitudes of the foces, they ae not ecto equations Fo static fiction, the equals sign is alid only at impeding motion, the sufaces ae on the ege of slipping Use the inequality if the sufaces ae not on the ege of slipping Foces of Fiction, final The coefficient of fiction depends on the sufaces in contact The foce of static fiction is geneally geate than the foce of kinetic fiction The diection of the fictional foce is opposite the diection of motion and paallel to the sufaces in contact The coefficients of fiction ae nealy independent of the aea of contact Static Fiction Static fiction acts to keep the object fom moing If F inceases, so does ƒ s If F deceases, so does ƒ s ƒ s µ s n Remembe, the equality holds when the sufaces ae on the ege of slipping 1

2 Kinetic Fiction The foce of kinetic fiction acts when the object is in motion Although µ k can ay with speed, we shall neglect any such aiations ƒ k = µ k n Exploe Foces of Fiction Vay the applied foce Note the alue of the fictional foce Compae the alues Note what happens when the can stats to moe Some Coefficients of Fiction Fiction in Newton s Laws Poblems Fiction is a foce, so it simply is included in the F in Newton s Laws The ules of fiction allow you to detemine the diection and magnitude of the foce of fiction Fiction Example, 1 The block is sliding down the plane, so fiction acts up the plane This setup can be used to expeimentally detemine the coefficient of fiction µ = tan Fo µ s, use the angle whee the block just slips Fo µ k, use the angle whee the block slides down at a constant speed Fiction, Example Daw the fee-body diagam, including the foce of kinetic fiction Opposes the motion Is paallel to the sufaces in contact Continue with the solution as with any Newton s Law poblem This example gies infomation about the motion which can be used to find the acceleation to use in Newton s Laws

3 Fiction, Example 3 Clicke Question Two blocks with diffeent masses, M1=1kg, and M=kg,, slide with the same constant speed on a smooth suface, then moe onto a suface haing fiction coefficient μ k. Which stops in the shote time? Fiction acts only on the object in contact with anothe suface Daw the fee-body diagams Apply Newton s Laws as in any othe multiple object system poblem A. M 1 B. M C. Both stop in the same time D. Cannot be detemined Lectue Quiz Two people, each of 70 kg mass, ae iding in an eleato. One is standing on the floo. The othe is hanging on a ope suspended fom the ceiling. Compae the foce F1 the floo exets on the fist peson to the foce F the ope exets on the second peson. Which statement is coect? A. They ae equal and opposite in diection. B. They ae equal and hae the same diection. C. F1 is geate than F, but they hae the same diection. D. F1 is geate than F, but they hae opposite diections. E. F1 is less than F, but they hae the same diection. Unifom Cicula Motion, Acceleation A paticle moes with a constant speed in a cicula path of adius with an acceleation: ac The centipetal acceleation, a c is diected towad the cente of the cicle The centipetal acceleation is always pependicula to the elocity Unifom Cicula Motion, Foce A foce, F, is associated with the centipetal acceleation The foce is also diected towad the cente of the cicle Applying Newton s Second Law along the adial diection gies F mac m Unifom Cicula Motion, cont A foce causing a centipetal acceleation acts towad the cente of the cicle It causes a change in the diection of the elocity ecto If the foce anishes, the object would moe in a staight-line path tangent to the cicle See aious elease points in the actie figue 3

4 Conical Pendulum The object is in equilibium in the etical diection and undegoes unifom cicula motion in the hoizontal diection F y = 0 T cos θ = mg F x = T sin θ = m a c is independent of m Lgsin tan Motion in a Hoizontal Cicle The speed at which the object moes depends on the mass of the object and the tension in the cod The centipetal foce is supplied by the tension T m Clicke Question A small ball is eleased fom est at position A and olls down a etical cicula tack unde the influence of gaity. When the ball eaches position B, which of the indicated diections most nealy coesponds to the diection of the nomal foce on the ball? A. 1 B. C. 3 D. 4 E. 5 Hoizontal (Flat) Cue The foce of static fiction supplies the centipetal foce The maximum speed at which the ca can negotiate the cue is g s Note, this does not depend on the mass of the ca Banked Cue These ae designed with fiction equaling zeo Thee is a component of the nomal foce that supplies the centipetal foce tan g Banked Cue, The banking angle is independent of the mass of the ehicle If the ca ounds the cue at less than the design speed, fiction is necessay to keep it fom sliding down the bank If the ca ounds the cue at moe than the design speed, fiction is necessay to keep it fom sliding up the bank 4

5 Loop-the-Loop This is an example of a etical cicle At the bottom of the loop (b), the upwad foce (the nomal) expeienced by the object is geate than its weight m F nbot mg nbot mg1 g Loop-the-Loop, Pat At the top of the cicle (c), the foce exeted on the object is less than its weight m F ntop mg ntop mg 1 g Non-Unifom Cicula Motion The acceleation and foce hae tangential components F poduces the centipetal acceleation F t poduces the tangential acceleation F F F t Vetical Cicle with Non- Unifom Speed The gaitational foce exets a tangential foce on the object Look at the components of F g The tension at any point can be found T mg cos Rg Top and Bottom of Cicle The tension at the bottom is a maximum T mg bot 1 Rg The tension at the top is a minimum T mg top 1 Rg If T top = 0, then top gr 5