Physics 111 Lectue 5 Cicula Motion D. Ali ÖVGÜN EMU Physics Depatment www.aovgun.com
Multiple Objects q A block of mass m1 on a ough, hoizontal suface is connected to a ball of mass m by a lightweight cod ove a lightweight, fictionless pulley as shown in figue. A foce of magnitude F at an angle with the hoizontal is applied to the block as shown and the block slides to the ight. The coefficient of kinetic fiction between the block and suface is μ k. Find the magnitude of acceleation of the two objects. Januay, 017
Multiple Objects q m1: q m: F F F x y F cos f T 0 T m g ma y m a y 1 N + F sin m g T m( a + g) N m1 g F sin k m a 1 x m a 1 Fcos f m ( a+ g) ma a k 1 Fcos f m g m k + m 1 Januay, 017
Unifom Cicula Motion: Definition Unifom cicula motion Constant speed, o, constant magnitude of velocity Motion along a cicle: Changing diection of velocity Januay, 017
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 Januay, 017
Januay, 017
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 π v v a c Januay, 017
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 Januay, 017 F net
What povide Centipetal Foce? q Centipetal foce is not a new kind of foce q Centipetal foce stands fo any foce that keeps an object following a cicula path ma 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 c mv Januay, 017
What povide Centipetal Foce? F net N mg ma N mg + m v F net T T mv ma a N mg Januay, 017
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) Januay, 017
Example 1:The Conical Pendulum q A small ball of mass m is suspended fom a sting of length L. The ball evolves with constant speed v in a hoizontal cicle of adius. Find an expession fo v and a m 5 kg L 5 m mg T F F y sin tan T T cos mg x T L cos mg sin ma 0.4 L 0.44 Januay, 017 c 0 mv m
Januay, 017 The Conical Pendulum 0.44 tan 0.4 sin sin cos 0 cos 5 5 L L mv T F mg T mg T F m m L kg m x y 4.3 m/s tan.9 m/s tan sin tan tan cos sin g v a Lg v g v g v mg T mv T q Find v and a
Example : The Effect of Speed on q Centipetal Foce The model aiplane has a mass of 0.90 kg and moves at constant speed on a cicle that is paallel to the gound. The path of the aiplane and the guideline lie in the same hoizontal plane because the weight of the plane is balanced by the lift geneated by its wings. Find the tension in the 17 m guideline fo a speed of 19 m/s. Januay, 017
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. Januay, 017
Januay, 017
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 in the centipetal foce equation o point 3, i.e. in Januay, 017
Poblem 1: Januay, 017
Poblem : Januay, 017
Poblem 3: Januay, 017
Poblem 4: Januay, 017
Poblem 5: Poblem 6: Januay, 017
Poblem 7: Januay, 017