动量碰撞质心平衡Arodoflength300cmhaslineardensity.DOC

動量、碰撞、質心、平衡 A rod of length 30.0 cm has linear density (mass-per-length) given by λ = 50.0 g/m + 20.0x g/m2 where x is the distance from one end, measured in meters. (a) What is the mass of the rod? (b) How far from the x = 0 end is its center of mass? 如圖6.1，質量M = 1.75 kg的木頭連結在k=40 N/m的彈簧上，一質量m = 0.25 kg的子彈以u = 24 m/s的速率射入木頭中（此過程木頭與地面無摩擦），然後木頭（含子彈）開始在粗糙的地面上滑動，若彈簧的最大壓縮量為0.5 m，求木頭所受的摩擦力為何？ 衝擊擺 (ballistic pendulum) 可用來測量子彈速度(如圖6.2)。若有一子彈質量m速度u射入質量M衝擊擺，使它上升了高度H。求出子彈初速度u。此問題滿足力學能守恆否，為什麼？此問題滿足線動量守恆否，為什麼？ Fig.6.3mMFig.6.2Fig.6.1Two blocks with masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them (Fig. 6.3). A cord initially holding the blocks together is burned; after this, the block of mass 3M moves to the right with a speed of 2.00 m/s. (a) What is the speed of the block of mass M? (b) Find the original elastic potential energy in the spring, taking M = 0.350 kg.  Fig.6.3 m M Fig.6.2 Fig.6.1 A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (Fig. 6.6). The angle between the two bonds is 106°. If the bonds are 0.100 nm long, where is the center of mass of the molecule? Fig.6.6Fig.6.7In Fig. 6-7, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 2.50 m and then collides with stationary block 2, which has mass m2=2.00m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.500 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic? Fig.6.6 Fig.6.7 (a) the conservation of the linear momentum何時會成立，只需判斷以下問題是否在某些方向滿足此原理 (需有理由)，不必去解出此問題：(b)小木塊自光滑三角形大木塊 (大木塊放在水平且光滑之桌面上)上由高處釋放下來。此問題動量守恆否？為什麼？(c)一砲彈發射至空中後爆炸成數片，此砲彈在爆炸瞬間，動量守恆否，為什麼？(忽略空氣阻力)，(c)測高速子彈之衝擊擺，動量守恆否，為什麼？(d)在湖泊上人由船尾走至船頭 (水之阻力可忽略)，動量守恆否，為什麼？ W, LmC圖6.8EADB相同的兩梯子AC、CE以60度角固定在可轉動的軸 C 點上，BD為一無質量的