Equilibrium of a particle一个粒子的平衡.docVIP

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Equilibrium of a particle一个粒子的平衡.doc

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Equilibrium of a particle一个粒子的平衡.doc

Equilibrium of a particle If all the forces acting on a particle cancel each other out, so that nothing happens at all, the forces are said to be in equilibrium. ( The algebraic sum of the horizontal components is zero. ( The algebraic sum of the vertical components is zero. Example 1 Find the value of P and Q if the following system of forces is in equilibrium. Solution Components diagram Horizontal component:( : 8 cos 30 + Q cos 40 ( P = 0 [1] Vertical component: ( : 8 sin 30 ( 2 ( Q sin 40 = 0 [2] ( Q sin 40 = 8 sin 30 ( 2 ( Q = 3.1114… Sub Q into [1]: 8 cos 30 + 3.114 cos 40 ( P = 0 ( P = 8 cos 30 + 3.114 cos 40 = 9.31 Force P is 9.31 N and force Q is 3.11 N Equilibrium of a particle *Example 2 Find the value of P and Q if the following system of forces is in equilibrium. Solution Components diagram Horizontal component:( : 8 cos 30 + Q cos 40 ( P cos 30 = 0 ( 0.866025 P = 6.928203 + 0.766044 Q ( P = 8 + 0.884552 Q [1] Vertical component: ( : 8 sin 30 + P sin 30 ( Q sin 40 = 0 ( Q sin 40 = 8 sin 30 + P sin 30 ( 0.642788 Q = 4 + 0.5 P [2] Sub P into [2]: 0.642788 Q = 4 + 0.5 (8 + 0.884552 Q) ( 0.642788 Q = 4 + 2 + 0.442276 Q ( 0.200512 Q = 6 ( Q = 29.9234 Sub Q into [1]: P = 8 + 0.884552 ( 29.9234 = 34.5 Force P is 34.5 N and force Q is 29.9 N Equilibrium of a particle Example The following diagram shows a system of forces acting on a particle in a plane. A third force is added so that the particle rests in equilibrium. Find the magnitude of this force and the angle that make with the horizontal. Solution Components diagram Horizontal component:( : 5 cos 30 + F cos( ( 6 = 0 ( F cos( = 6 ( 5 cos 30 [1] Vertical component: ( : 5 sin 30 ( F sin( = 0 ( F sin( = 5 sin 30 [2] Divide [2] by [1]: ( ( = 56.2591 Sub ( into [2]: F sin 56.2591 = 2.5 ( F = 3.00 Added force is 3.