Physics 101 Lecture 6 Circular Motion
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1 Physics 101 Lectue 6 Cicula Motion Assist. Pof. D. Ali ÖVGÜN EMU Physics Depatment
2 Equilibium, Example 1 q What is the smallest value of the foce F such that the.0-kg block will not slide down the wall? The coefficient of static fiction between the block and the wall is 0..? N f F F mg
3 Unifom Cicula Motion: Definition Unifom cicula motion Constant speed, o, constant magnitude of velocity Motion along a cicle: Changing diection of velocity
4 Unifom Cicula Motion: Obsevations q Object moving along a cuved path with constant speed n Magnitude of velocity: same n Diection of velocity: changing n Velocity v! : changing n Acceleation is NOT zeo! n Net foce acting on an object is NOT zeo n Centipetal foce!! F ma net
5 Unifom Cicula Motion q Velocity: n Magnitude: constant v n The diection of the velocity is tangent to the cicle q Acceleation: n Magnitude: v a c n diected towad the cente of the cicle of motion q Peiod: n time inteval equied fo one complete evolution of the paticle T!! a c ^ v p v v a c
6 Centipetal Foce q Acceleation: n Magnitude: n Diection: towad the cente of the cicle of motion q Foce: n Stat fom Newton s nd Law!! F net ma n Magnitude: F net v a c ma mv n Diection: towad the cente of the cicle of motion c!! a c ^ v v a c F! net!! F net ^ v F! net!! a c F net F! net
7 What povides Centipetal Foce? q Centipetal foce is not a new kind of foce q Centipetal foce efes to any foce that keeps an object following a cicula path q Centipetal foce is a combination of n Gavitational foce mg: downwad to the gound n Nomal foce N: pependicula to the suface n Tension foce T: along the cod and away fom object n Static fiction foce: f s max µ s N F c ma c mv
8 What povides Centipetal Foce? F net N - mg ma N mg + m v F net T T mv ma a N v mg
9 Poblem Solving Stategy q Daw a fee body diagam, showing and labeling all the foces acting on the object(s) q Choose a coodinate system that has one axis pependicula to the cicula path and the othe axis tangent to the cicula path q Find the net foce towad the cente of the cicula path (this is the foce that causes the centipetal acceleation, F C ) q Use Newton s second law n n The diections will be adial, nomal, and tangential The acceleation in the adial diection will be the centipetal acceleation q Solve fo the unknown(s)
10 Vetical Cicula Motion q In vetical cicula motion the gavitational foce must also be consideed. An example of vetical cicula motion is the vetical loop-the-loop motocycle stunt. Nomally, the motocycle speed will vay aound the loop. q The nomal foce, FN, and the weight of the cycle and ide, mg, ae shown at fou locations aound the loop.
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12 Thee is a minimum speed the ide must have at point 3 in ode to stay on the loop. This speed may be found by setting centipetal foce equation o point 3, i.e. in in the
13 Poblem :
14 Ex: The Conical Pendulum q A small ball of mass m 5 kg is suspended fom a sting of length L 5 m. The ball evolves with constant speed v in a hoizontal cicle of adius m. Find an expession fo v and a. T θ mg
15 The Conical Pendulum 0.44 tan 0.4 sin sin cos 0 cos å å L L mv T F mg T mg T F m m L kg m x y q q q q q 4.3 m/s tan.9 m/s tan sin tan tan cos sin q q q q q q q g v a Lg v g v g v mg T mv T q Find v and a
16 Ex:3 Level Cuves q A 1500 kg ca moving on a flat, hoizontal oad negotiates a cuve as shown. If the adius of the cuve is 35.0 m and the coefficient of static fiction between the ties and dy pavement is 0.53, find the maximum speed the ca can have and still make the tun successfully. v µ g
17 Level Cuves q The foce of static fiction diected towad the cente of the cuve keeps the ca moving in a cicula path. f N v s,max å max F y v µ sn m N - mg 0 mg µ sn m (0.53)(9.8m / s v µg max µ smg m )(35.0m) µ g s 13.4m / s
18 Ex:4 Banked Cuves q A ca moving at the designated speed can negotiate the cuve. Such a amp is usually banked, which means that the oadway is tilted towad the inside of the cuve. Suppose the designated speed fo the amp is to be 13.4 m/s and the adius of the cuve is 35.0 m. At what angle should the cuve be banked?
19 Banked Cuves v 13.4 m/s å å tanq q F F y ncosq mg tan mv nsinq mac n cosq - mg 0 v g -1 ( 35.0 m 13.4 m/s (35.0 m)(9.8 m/s ) )! 7.6
20 Poblem 1: ANS: Fo A : T0.058 N, Fo C: T0.58 N
21 Poblem : Poblem 3: R5.5m v4 m/s
22 Poblem 4: R39.4 m Poblem 5: v4.1 m/s
23 Poblem 6: A sting unde a tension of 50.0 N is used to whil a ock in a hoizontal cicle of adius.50 m at a speed of 0.4 m/s on a fictionless suface as shown in Figue. As the sting is pulled in, the speed of the ock inceases. When the sting on the table is 1.00 m long and the speed of the ock is 51.0 m/s, the sting beaks. What is the beaking stength, in newtons, of the sting? Poblem 7: A puck of mass m1 is tied to a sting and allowed to evolve in a cicle of adius R on a fictionless, hoizontal table. The othe end of the sting passes though a small hole in the cente of the table, and an object of mass m is tied to it Fig. The suspended object emains in equilibium while the puck on the tabletop evolves. Find symbolic expessions fo (a) the tension in the sting, (b) the adial foce acting on the puck, and (c) the speed of the puck.
24 Poblem 8: Poblem 9:
25 Poblem 10: Poblem 11:
26 Poblem 1:
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