Rectilinea Motion. A foce P is applied to the initially stationay cat. Detemine the velocity and displacement at time t=5 s fo each of the foce histoi

Size: px

Start display at page:

Download "Rectilinea Motion. A foce P is applied to the initially stationay cat. Detemine the velocity and displacement at time t=5 s fo each of the foce histoi"

Stephen Page
5 years ago
Views:

1 Rectilinea Motion 1. Small objects ae deliveed to the m inclined chute by a conveyo belt A which moves at a speed v 1 =0.4 m/s. If the conveyo belt B has a speed v =0.9 m/s and the objects ae deliveed to this belt with no slipping, calculate the coefficient of fiction m k between the objects and the chute.

2 Rectilinea Motion. A foce P is applied to the initially stationay cat. Detemine the velocity and displacement at time t=5 s fo each of the foce histoies P 1 and P. eglect fiction.

3 Rectilinea Motion 3. The slides A and B ae connected by a light igid ba and move with negligible fiction in the slots, both of which lie in a hoizontal plane. o the position shown, the velocity of A is 0.4 m/s to the ight. Detemine the acceleation of each slide and the foce in the ba at this instant.

4 Rectilinea Motion 4. The colla slides down the od. The coefficient of fiction is m k = The tension in the cable attached to the colla is constant as 80 and the angle between the cable and the hoizontal emains the same as a thoughout the motion. The weight of the colla is 60. If the colla stops afte 10 seconds it stats sliding down the od with an initial velocity of 5 m/s, what should a be?

Cuvilinea Motion 5. The pin P is foced to move in the fied paabolic slot by the moving vetical guide. The centeline of the slot is descibed by y = 0.015 [mm].

5 Cuvilinea Motion 5. The pin P is foced to move in the fied paabolic slot by the moving vetical guide. The centeline of the slot is descibed by y = [mm]. When = 40 mm, the speed v of the guide is 100 mm/s and is not changing at this instant. Detemine the magnitudes and R of the foces which the guide and the vetical plate, espectively, eet on the 50 g pin.

6 Cuvilinea Motion 6. A 0.8-kg slide is popelled upwad at A along the fied cuved ba which lies in a vetical plane. If the slide is obseved to have a speed of 4 m/s as it passes position B, detemine, (a) the magnitude of the foce eeted by the fied od on the slide and (b) the ate at which the speed of the slide is inceasing. Assume that fiction is negligible.

7 omal&tangential Coodinates BD mg + t KD ma t + t + n ma n + n ma n ma mg cos 30 ma n n t v ma t, ma mg cos 30 ma cos n n n t ma t mg sin 30 ma t a t m / s a t

Cuvilinea Motion 7. The small object is placed on the inne suface of the conical dish at the adius shown. If the coefficient of static fiction between the object and the conical suface is 0.

8 Cuvilinea Motion 7. The small object is placed on the inne suface of the conical dish at the adius shown. If the coefficient of static fiction between the object and the conical suface is 0.30, fo what ange of angula velocities w about the vetical ais will the block emain on the dish without slipping? Assume that speed changes ae made slowly so that any angula acceleation may be neglected.

9 Cuvilinea Motion 8. The 1 kg colla slides along the smooth paabolic od in the vetical plane towad point O. The sping whose stiffness is k=600 /m has an unstetched length of 1 m. If, at the position shown in the figue, velocity of the colla is 3.5 m/s, detemine the foce acting on the colla by the paabolic od fo this instant. eglect the fiction.

10 Cuvilinea Motion 10. The slotted am evolves in the hoizontal plane about the fied vetical ais though point O. The kg slide C is dawn towad O at the constant ate of 50 mm/s by pulling the cod S. At the instant fo which =5 mm, the am has a counteclockwise angula velocity w=6 ad/s and is slowing down at the ate of ad/s. o this instant, detemine the tension T in the cod and the magnitude of the foce eeted on the slide by the sides of the smooth adial slot. Indicate which side, A o B, of the slot contacts the slide.

Pola Coodinates (Hoizontal plane) KD BD + + ma ma T 5 mm, 0.

11 Pola Coodinates (Hoizontal plane) KD BD + + ma ma T 5 mm, m / s ( constant ), 6 ad / s, ad / s ma ma T ma, T m ma 16. ma (Side B)

12 Cuvilinea Motion 11. The 1.5 kg cylinde C tavels along the path descibed by =(0.6sin ) [mete]. If am OA otates counte clockwise with a constant angula velocity of =3 ad/s, detemine the foce eeted by the smooth slot in am OA on the cylinde at the instant = 60. The sping has a stiffness of 100 /m and is unstetched when =30. Motion occus in the vetical plane.

13 Cuvilinea Motion 13. The slotted am is used to move the smooth 0.5 kg paticle P aound the vetical path in the shape of a limaçon with = 0.3 ( + cos ) m. The sping with a stiffness of k = 8 /m in the slot ensues that the paticle P does not lose contact with the path. The sping is unstetched when is eual to 90. If = (0.5t ) ad, whee t is in seconds, detemine the foces and which the od and the slotted am, espectively, eets on the paticle at the instant t = 1.5 s. 0.6 m 0.9 m

14 Cuvilinea Motion 1. The 1 kg ball A, which slides in a slot in the otating am OB, is kept in contact with the stationay cam C by a y =0.1(+cos ) m B sping. The sping has a stiffness of 1000 /m and is unstetched when 0. m A the am OB is in position OP. If the am otates with the constant angula P Q velocity =0 ad/s (ccw), calculate C the nomal foce which the cam eets on A and also the foce R 0.1 m 0.3 m eeted on A by the sides of the slot when =30 o. All sufaces ae smooth. The poblem occus in vetical plane.

15 + R 30 o mg + 30 o +n b sping 0. m y =0.1(+cos ) m B A b? Kinematics P Q v e e 0. 1 cos m 0. 1 sin 1 m / s m / s v 1e 5. 73e C 0.1 m 0.3 m

16 +t v + v b actan o b + v b 30 o +n a a a sin cos m / s 0 0 cos m / s m / s

17 + R 30 o mg + The sping is unstetched when the am OB is in position OP. =0.1 m when the sping is unstetched. =0.86 m when =30 o. 30 o b sping sping k n ma sin 30 cos mg sin 30 cos 9. 9 sping ma ma cos sin 9. 9 R 1 40 R mg cos 30 sin 9. 9 R ma

18 Cuvilinea Motion 9. The hoizontal platfom is otating with a constant angula velocity of w=5 ad/s. Two identical blocks, each with a mass of kg ae held in the smooth slot within the platfom by a pai of spings each with a stiffness of k=50 /m. If the unstetched length of each sping is l o = 0.18 m, what should angle be fo steady state position? Spings ae attached to the platfom at point A. (Conside only one block fo the solution of the poblem.)

19 W w= 5 ad/s, m = kg ma cos sping sin m y R sping cicula motion, steady state position sp k cos k sin sin sin ma sping sping cos k sin m cos m cos k cos w y 0.3 m sping sin

20 w y cos cos sin k k m sin k cos k sin m sin Putting into cos sin m sin k 1 sin 0.3 m sping k sin sin 50 sin 0.5 sin tan cos final m sin sin sin length initial, 0.75 sin length 00 sin sin sin 0.18

21 Cuvilinea Motion 10. The pin P is foced to move in the fied paabolic slot by the moving vetical guide. The centeline of the slot is descibed by y = [mm]. When = 40 mm, the speed v of the guide is 100 mm/s and is not changing at this instant. Detemine the magnitudes and R of the foces which the guide and the vetical plate, espectively, eet on the 50 g pin.

22 mg +n 1 slot paabolic on P by acting oce guide vetical on P by acting oce d dy o : : tan 1 40 Kinematics: j a s mm y a v j i v s mm y y P P dt d 300 / 300 0) (100 ) 0.03( 0 constant / (40)(100) Kinetics: (0.3) cos (0.05)(9.81) cos sin 0 sin y y y ma mg ma ma

Physics 111 Lecture 5 Circular Motion

Physics 111 Lecture 5 Circular Motion 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