理论力学摩擦4.pptVIP

1 1 所以物体运动：此时 Hence, when the body begin to move （物体已运动） (the body already moves) 1 [Exercise 2] Let the weight of block A be 500N, the weight of the roller B is 1000N, the roller D is smooth, the coefficient of friction at points E and A are fE=0.2, fA=0.5. Determine the weight of the block C, Q=?, when the system is in equilibrium. [练习2] 已知A块重500N，轮B重1000N，D轮无摩擦，E 点的摩擦系数fE=0.2，A点的摩擦系数fA=0.5。 求：使物体平衡时块C的重量Q=？ 1 由于 1 解：① A不动（即i点不产生 平移）求Q Solution: ① A does not move(i.e., point i has no translation), determine Q. 1 Investigate the roller: 分析轮有 From 由 1 1 ②There is no horizontal displacement at point E, hence ② E 点不产生水平位移 1 1 ③ The roller B does not move upwards, hence N≥0. ③ B轮不向上运动，即N≥0 1 显然,如果i,E两点均不产生运动,Q必须小于208N,即 Obviously, if there is no motion of both points i and E, Q must be less than 208N, hence 1 ① ② Additional equation ③ 补充方程 ③ Solution: ①Investigate the whole system: 解： ①研究整体 [Exercise 3] P, D, d, Q1 and Q2 are known, P is horizontal. Determine f when the bigger ball rolls across the smaller one. [练习3] 已知：P、D、d、Q1、Q2，P为水平。 求：在大球滚过小球时，f=? 1 要保证大球滚过小球，必须使大球与小球之间不打滑 The bigger ball can not roll across the smaller ball unless we can ensure that the bigger ball can not slip on the smaller ball. ∴当 时，能滚过去（这是小球与地面的f 条件） ∴If , the bigger ball can roll across the smaller one. Substituting ① and ② into ③ ,we get: 将①、②代入③得： 1 ②Determine f between the balls, investigate the bigger ball: ① ② ②求大球与小球之间的f , 研究大球 1 补充方程 ③ Additional equation: 将③代入②得： ④ Substituting ③ into ② we have: ④ Again 1 Conclusion:When both and are satisfied the bigger ball can roll across the smaller one. 结论：当 和 时能保证大球能滚过小 球的条件。 Solving ④ we find: 解④得： ∴If , the bigger ball can roll across the small one. ∴当 时能