For the three forces. find: (a) the resultant force R~ (a) (b) the magnitude of the resultant force. Three coplanar forces, A
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1 WorkSHEE 8. Vector applcatons ame: or the three forces, and, fnd: the resultant force R R the mantude of the resultant force. R hree coplanar forces,, B and C have mantudes of 8, 6 and 9 respectvely. nd the anle between B and C f the resultant force s zero. or Usn the cosne rule: ( (9 (6 cos 8! q ( 8 cos 8! q 7 8 cosq 8 cosq 5 5 cosq 8.97 q 9. he anle between forces B and C s 9.. John Wley & Sons ustrala, Ltd 9
2 Maths Quest Maths C Year for Queensland Chapter 8: Vector applcatons WorkSHEE 8. boy pulls a cart alon by an attached rope. he cart s on a horzontal path and the rope makes an anle of to the horzontal. If the rope exerts a force of mantude on the cart, fnd: the horzontal component of the force exerted on the cart by the rope Horzontal component cos the vertcal component of the force exerted on the cart by the rope. Vertcal component sn.5 mass of k rests on a horzontal table. If the coeffcent of frcton s.5, what s the mantude of the least force that wll move the obect? If hen and μ k mass s held on a smooth nclned plane, anled at 5 to the horzontal, by a strn that s parallel to the plane. Draw a vector force daram shown the forces actn on the mass. nd the mantude of the resultant force, R. Snce the mass s not movn, the forces are n equlbrum. R Wow, that s a stupd queston, of course the resultant vector s zero, because t sn t moven! Lets ask the queston the text book should have asked next. John Wley & Sons ustrala, Ltd 9
3 Maths Quest Maths C Year for Queensland Chapter 8: Vector applcatons WorkSHEE 8. 6 k mass s held on a smooth nclned plane, anled at 5 to the horzontal, by a strn that s parallel to the plane. Draw a vector force daram shown the forces actn on the mass. nd the tenson on the strn. hat daram s a bt useless ts easer to see f you draw the and vectors n a new daram makn a rht anled tranle wth the W eht vector. See nney f you need! 9.6 cos or the stuaton descrbed n the prevous queston, use as a unt vector up the plane and 9.6 sn 5.86 herefore the tenson on the strn s.86 ewtons. s at rht anles to as a unt vector perpendcular to the plane to fnd: the weht vector W usn notaton the tenson force n the strn, usn notaton W sn 5 R Snce R cos 5 ( ( (c the mantude of the normal contact force,. (c John Wley & Sons ustrala, Ltd 9
4 Maths Quest Maths C Year for Queensland Chapter 8: Vector applcatons WorkSHEE 8. 6.k mass rests on a plane nclned at such that t s ust about to slde. 5 he plane s then nclned at an anle of 6. Determne the resultant force on the mass. R But R. sn. cos herefore µ (. sn (. cos. sn cos ow R (. sn6 (. cos6. cos6. cos6 9. µ 9..5! Resultant force. cos 6.56 John Wley & Sons ustrala, Ltd 9
5 Maths Quest Maths C Year for Queensland Chapter 8: Vector applcatons WorkSHEE 8. John Wley & Sons ustrala, Ltd wo masses, k and k m m, connected by a lht, nextensble strn, are pulled by a horzontal force,. he force s appled to m and the connected masses slde across a horzontal table at constant speed. If the coeffcent of frcton s.5, determne: the mantude of the tenson n the strn the mantude of. ( ( (constant speed : or Þ a R m (.5 µ ( ( : or R m.9.5 µ Substtutn nto equaton (:
6 Maths Quest Maths C Year for Queensland Chapter 8: Vector applcatons WorkSHEE 8. 8 horzontal force of 6 acts on a.5k block resultn n unform moton across a flat floor. nd the coeffcent of frcton. ( 6 (. R 5 Snce moton s unform (that s, velocty s constant, R 6 6 and.5.5 µ 6.5».9 he coeffcent of frcton s approxmately.9. 9 he follown three forces are n equlbrum, and. Calculate. \ ( ( 5 John Wley & Sons ustrala, Ltd 9 6
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