理论力学课后习题答案

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,理论力学,复习题库,题,1,3,xy,坐标系下：,投影：,分力的大小：,F,x,F,y,F,x,F,y,在,直角坐标系,下，力沿坐标轴的分力的大小,等于,力在相应坐标轴上投影的绝对值。,题,1,3,续,1,x,y,坐标系下：,投影：,分力的大小：,在,非直角坐标系,下，力沿坐标轴的分力的大小,不等于,力在相应坐标轴上投影的绝对值。,F,y,F,x,F,y,F,x,题,1,3,续,2,x,y,坐标系下：,分力的大小也可按,正弦定理,来计算：,F,y,F,x,题,1,6,采用,合力矩定理,采用,力矩定义,a,r,2,d,A,r,1,F,F,题,1,10,1,1,4,F,x,F,y,F,z,分力的大小：,采用,合力矩定理,题,1,10,续,力的作用点坐标：,x,1,，,y,1,，,z,0,采用,解析计算公式,力的投影,：,F,1,1,4,题,1,12,F,A,x,F,A,y,M,A,F,A,x,F,A,y,F,C,F,B,F,A,题,1,13,F,A,x,F,A,y,F,D,F,C,F,C,F,A,x,F,A,y,F,D,F,B,C,BC,AB,整体,F,B,x,F,B,y,F,B,x,F,B,y,B,A,D,题,1,13,续,1,BD,AB,滑轮,整体,F,A,x,F,A,y,F,B,A,C,B,F,C,x,F,C,y,F,D,B,D,F,B,C,P,F,C,x,F,C,y,F,F,A,x,F,A,y,F,F,D,题,1,13,续,2,A,C,D,BC,AC,整体,F,F,A,F,C,x,F,C,y,F,D,C,E,B,F,C,x,F,C,y,F,B,F,E,F,A,F,B,题,2,1,y,x,O,F,R,平面汇交力系,题,2,4,平面力偶系,题,2,13,x,y,主矢：,对,A,点的,主矩：,力系存在,合力,题,2,16,主矢：,对,O,点的,主矩：,5,题,2,18(b),形心在对称轴,y,上,1,2,C,2,C,1,题,3,7,空间汇交力系,独立的平衡方程有,3,个,F,AD,F,AB,F,AO,a,a,2,a,点,A,题,3,9,平面力偶系,独立的平衡方程有,1,个,F,D,F,A,整体,BCD,是,二力杆,题,3,14(a),平面力系,F,Ax,F,Ay,F,B,独立的平衡方程有,3,个,整体,题,3,15(b),物体系统平衡,F,Bx,F,C,F,By,B,C,BC,整体,q,F,Ax,F,C,F,Ay,M,A,题,3,16(d),BC,整体,F,Ax,F,Ay,F,Bx,F,By,B,C,F,Cx,F,Cy,F,Bx,F,By,q,整体,题,3,25,空间力系,F,Ax,F,G,F,Ay,F,Az,F,H,整体,C,题,3,17(b),F,E,F,A,F,FG,F,Cx,F,E,F,Cy,G,F,FG,F,BG,F,AG,整体,CEF,铰,G,组合结构,E,C,F,F,D,对称性,题,3,19,q,2,E,C,F,Cx,F,Cy,F,E,DE,BD,M,A,F,Ax,F,Ay,F,E,F,D,q,1,B,C,D,F,Bx,F,By,F,D,F,C,x,F,C,y,题,3,19,续,M,A,F,Ax,F,Ay,F,E,F,D,整体,题,3,22,OA,O,1,A,O,A,M,1,F,O,F,A,O,1,A,F,O,1,F,A,M,2,题,4,6,F,F,N,设坝不滑动,而,假设成立,坝不滑动,设坝不绕,B,点转动,x,F,F,N,E,假设成立,坝不绕,B,点转动,假设坝静止不动,而,坝不滑动,x,F,F,N,E,假设成立,坝不绕,B,点转动,坝既不滑动，也不绕,B,点转动。,题,4,6,题,4,7,F,2,F,1,F,N2,F,N1,活动支架,补充方程,求安全工作时的,x,设活动支架处于,临界状态,A,题,4,8,A,B,F,AC,F,BC,F,F,B,F,N,B,P,B,F,BC,F,A,F,N,A,P,A,F,AC,C,C,A,B,维持平衡的最大力,A,题,4,9,求保持系统平衡的最小力,F,1,设物块,B,处在下滑还未滑动的,临界状态,物块,尖劈,补充方程,B,P,F,s,F,N1,F,N,F,1,F,N2,F,N,F,s,A,题,4,9,续,求保持系统平衡的最大力,F,2,设物块,B,处在上滑还未滑动的,临界状态,物块,尖劈,补充方程,B,P,F,s,F,N1,F,N,F,2,F,N2,F,N,F,s,题,4,12(a),F,A,F,C,y,F,C,x,C,A,F,AB,F,AD,F,A,D,F,BC,F,CD,F,C,y,F,C,x,整体,F,CD,600,N,F,AD,F,BD,C,A,D,F,2,F,7,F,9,F,10,题,4,14(c),B,F,3,F,1,A,F,4,F,5,mm,截面：,m,m,n,n,nn,截面：,F,2,F,7,F,6,F,8,B,B,j,直角坐标法,2,j,题,5,6,j,自然法,2,j,s,O,1,题,5,6,续,题,5,9,题,5,14,运动方向发生改变,点位于,AO,上,揉桶作曲线平移,题,6,4,题,6,7,w,a,题,6,11,a,At,v,A,1,、,2,轮接触点速度相同,1,、,2,轮接触点,切向,加速度相同,O,1,A,、,O,2,B,、,轮,2,作定轴转动,AB,连同轮,1,作曲线平移,w,2,a,2,题,7,3,动点：,A,（,在,AB,上,）,动系：偏心轮,静系：地面,v,A,=,v,e,+,v,r,绝对运动：,圆周运动,(,B,),相对运动：,圆周运动,(,C,),牵连运动：,定轴转动,(,O,),w,1,q,v,A,v,r,v,e,题,7,7,动点：套筒,A,动系：,BCE,， 静系：地面,绝对运动：,圆周运动,(,O,),相对运动：,直线运动,(,),牵连运动：,直线平移,( ),v,A,v,r,v,e,v,A,=,v,e,+,v,r,j,w,题,7,11,动点：销钉,K,（,在,AB,上,）,动系：杆,OC,静系：地面,v,K,v,r,v,e,v,K,=,v,e,+,v,r,绝对运动：,直线运动,( ),相对运动：,直线运动,( ),牵连运动：,定轴转动,(,O,),w,1,j,1,题,7,14,动点：滑块,A,动系：滑杆,BC,静系：地面,绝对运动：,圆周运动,(,O,),相对运动：,圆周运动,(,O,1,),牵连运动：,直线平移,( ),1,v,A,=,v,e,+,v,r,v,A,v,e,v,r,a,e,a,rt,a,rn,a,A,y,a,A,=,a,e,+,a,rn,+,a,rt,题,7,15,动点：,A,（,在,OA,上,）,动系：,BC,静系：地面,绝对运动：,圆周运动,(,O,),相对运动：,直线运动,(,),牵连运动：,直线平移,( ),v,A,v,e,v,r,v,A,=,v,e,+,v,r,a,A,=,a,e,+,a,r,a,A,a,e,a,r,题,7,16,动点：,A,（,在,BC,上,）,动系：凸轮， 静系：地面,绝对运动：,直线运动,( ),相对运动：,圆周运动,(,O,),牵连运动：,直线平移,( ),v,A,=,v,e,+,v,r,v,A,v,e,v,r,j,x,a,A,=,a,e,+,a,rn,+,a,rt,投影,a,A,a,rt,a,rn,a,e,题,7,18,动点：小环,M,动系：,OBC,静系：地面,绝对运动：,直线运动,( ),相对运动：,直线运动,( ),牵连运动：,定轴转动,(,O,),v,M,v,e,v,r,j,v,M,=,v,e,+,v,r,a,M,=,a,e,+,a,r,+,a,C,a,M,a,e,a,r,j,a,C,y,投影,题,7,19,动点：,M,动系：圆盘， 静系：地面,绝对运动：,曲线运动,相对运动：,直线运动,( ),牵连运动：,定轴转动,(,AB,),a,r,a,M,=,a,en,+,a,et,+,a,r,+,a,C,a,en,v,r,x,z,y,a,et,a,C,v,rn,时：,a,et,x,a,C,x,题,7,19,续,动点：,M,动系：圆盘， 静系：地面,绝对运动：,曲线运动,相对运动：,直线运动,( ),牵连运动：,定轴转动,(,AB,),a,r,a,M,=,a,en,+,a,et,+,a,r,+,a,C,a,en,v,r,x,z,y,a,et,a,C,v,rn,a,et,x,a,C,x,题,7,20,动点：水点，动系：圆环， 静系：地面,绝对运动：,曲线运动,相对运动：,圆周运动,(,O,1,),牵连运动：,定轴转动,(,O,),a,=,a,e,+,a,r,+,a,C,a,e,v,r,a,C,a,r,v,r,a,C,a,r,y,a,e2,B,x,y,A,0,K,0,K,q,纯滚动,以,A,为基点,题,8,2,题,8,8,v,A,w,ABC,I,v,B,v,D,5,cm,10,cm,5,cm,杆,O,1,A,、,O,2,B,定轴转动,板,ABD,平面运动,题,8,12,v,2,w,2,I,v,w,1,杆,O,1,O,2,、轮,O,1,定轴转动,轮,O,2,平面运动,轮,O,1,与轮,O,2,在接触点处的速度,q,v,A,v,B,v,D,I,AB,D,2,D,1,w,OB,w,AB,w,I,题,8,13,题,8,16,v,A,I,w,B,v,B,v,C,AB,瞬时平移,轮,只滚不滑,B,点作,圆周运动,a,A,a,B,n,a,B,t,a,BA,t,x,y,a,CB,n,0,0,0,90,O,60,O,v,A,v,B,I,AB,w,AB,I,BC,v,C,w,BC,题,8,18,90,O,60,O,a,A,a,B,a,BA,t,a,BA,n,x,a,B,=,a,A,+,a,BA,n,+,a,BA,t,a,C,=,a,B,+,a,CB,n,+,a,CB,t,a,CB,t,a,CB,n,a,C,y,x,：,a,B,cos60,o,a,A,cos60,o,a,BA,n,y,：,a,C,a,B,sin60,o,a,CB,n,题,8,18,续,I,w,1,w,动点：,B,（在轮上）,动系：,O,1,A,；静系：地面,v,B,=,v,e,+,v,r,题,8,21,BIO,1,是等边三角形,v,B,v,e,v,r,a,B,=,a,O,+,a,BO,n,+,a,BO,t,=,a,BO,n,v,O,=,常量,a,O,=,0,a,=,a,O,/,OI,=,0,a,B,=,a,en,+,a,et,+,a,r,+,a,C,a,BO,n,=,a,en,+,a,et,+,a,r,+,a,C,I,a,BO,n,a,r,a,et,a,en,a,C,a,1,x,x,：,a,BO,n,a,et,a,C,题,8,21,续,m,g,F,N,F,a,n,e,n,钢球,钢球脱离圆筒时,题,10,4,m,A,g,F,N,A,2,F,T,F,A,m,B,g,F,N,B,3,F,T,F,B,a,A,a,B,求导,题,10,6,m,g,F,N,a,t,a,n,代入 ,F,N,0,变量分离,题,10,8,x,y,F,x,P,W,F,y,整体,动量定理,题,11,4,还可用,质心运动定理,解,x,y,F,x,P,W,F,y,整体,v,C,v,动量定理,题,11,4,续,x,y,v,A,v,B,v,e,v,r,动点：,A,动系：,B,，静系：地面,题,11,11,x,y,C,q,P,F,N,题,11,6,x,y,C,q,P,F,N,题,11,6,续,F,x,F,y,a,C,n,a,C,t,x,y,质心运动定理,题,11,7,x,y,题,11,14,F,x,x,题,11,17,题,11,18,F,x,v,1,v,2,题,12,1,F,F,y,W,1,F,x,W,2,在平衡位置：,微小摆动,题,12,5,t,=0,时，,j,0,=,d,0,/,l,，,j,0,=0,F,F,y,W,1,F,x,W,2,A,、,b,题,12,5,续,圆台和物块,z,初瞬时,任一瞬时,求导,题,12,9,w,B,v,w,C,F,F,B,y,F,B,x,P,1,F,C,y,F,C,x,F,P,2,AB,C,题,12,12,W,1,F,A,y,F,A,x,W,2,W,3,w,B,v,C,w,A,v,B,I,整体,题,12,17,a,C,a,C,a,I,x,y,W,F,max,F,N,F,也可用,对速度瞬心的,动量矩定理,求解,题,12,21,W,F,F,N,a,I,w,a,C,n,a,C,t,v,C,题,12,22,A,W,F,N,a,C,x,a,a,C,y,a,CA,t,a,A,F,N,F,A,y,F,A,x,F,质量不计,整体,题,12,25,轮,题,13,1,I,w,v,2,v,v,= 0,w,或者,题,13,5,2,v,v,= 0,w,题,13,5,链接,返回,O,B,A,w,AB,I,AB,I,B,C,v,C,w,B,v,B,v,A,w,OA,m,1,g,m,1,g,题,13,12,题,13,13,v,A,F,F,N,W,P,F,x,F,y,a,A,v,O,w,I,求导,v,B,v,A,I,AB,w,AB,v,C,求导,题,13,14,椭圆规尺位于,水平面内,F,F,N,m,g,w,a,v,C,a,C,t,a,C,n,I,题,13,19,求导,F,F,N,m,g,w,a,v,C,a,C,t,a,C,n,I,或,题,13,19,续,圆盘与杆一起绕,O,点,定轴转动,v,C,v,1,题,13,21,(a),C,v,C,v,1,杆,定轴转动,，圆盘,？,m,1,g,F,y,F,x,a,圆盘,平移,题,13,21,续,(b),m,g,F,y,F,x,w,a,C,t,a,C,n,求导,题,13,23,m,g,w,0,v,C,0,x,y,圆盘,平面运动,题,13,23,续,F,x,F,y,m,1,g,m,2,g,v,v,s,求导,a,a,x,A,、,B,及轮：,动量矩定理求,a,；,整体：,质心运动定理求,F,x,题,13,24,F,y,F,x,F,N,m,1,g,m,2,g,w,v,整体,S,求导,或者,动量矩定理求,a,题,13,26,F,y,F,x,F,N,m,1,g,m,2,g,a,a,轮,F,F,F,题,13,26,续,a,C,t,a,C,n,M,I,C,F,I,n,F,I,t,向点,C,简化：,a,C,t,a,C,n,F,I,n,F,I,t,M,I,A,向点,A,简化：,题,14,1,A,B,杆,AB,a,P,F,A,x,F,BC,F,A,y,3,4,5,F,I,杆,平移,题,14,4,题,14,6,W,F,y,F,x,a,C,n,a,C,t,w,a,F,I,n,F,I,t,M,I,O,积分,题,14,6,续,W,F,y,F,x,a,C,n,a,C,t,w,a,F,I,n,F,I,t,M,I,O,题,14,7,B,A,F,3,F,2,M,m,1,g,m,2,g,a,a,M,I,F,I,轮、物块,B,A,n,n,M,m,1,g,m,2,g,M,I,F,I,F,4,F,1,F,5,nn,截面右侧,a,e,a,r,a,n,a,t,动点：,C,，,动系：,ABC,，,静系：地面。,轮,平面运动,，杆,平移,。,x,题,14,10,P,F,x,F,C,F,y,a,ABD,m,g,F,N,F,C,F,max,M,I,F,I,轮,杆,题,14,10,续,W,F,C,A,a,C,a,a,A,C,a,A,t,a,CA,t,x,M,I,F,I,a,C,杆,平面运动,题,14,12,W,F,C,A,a,C,a,x,M,I,F,I,题,14,12,续,M,I,F,I,m,g,F,F,N,a,O,a,y,题,14,15,F,I,D,F,I,E,x,y,z,a,E,a,D,F,B,x,F,B,y,F,A,y,F,A,x,F,A,z,空间力系,平衡,题,14,16,