Week 11-Dynamics - Impact 1 In the case of central impact...

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1Impact 1.In the case of central impact, two colliding bodies Aand Bmove along the line of impact velocities (vA)1and (vB)1, respectively. Two equations can be used to determine their velocities (vA)2and (vB)2after the impact. The first represents the conservation of the total linear momentum of the two bodies along the line of impact, ((((2211BBAABBAAvmvmvmvm+=+The second equation relates the relative velocities of the two bodies before and after impact, (((([].1122BAABvvevv-=-The constant eis known as the coefficient of restitution; its value lies between 0 and 1 and depends on the materials involved. When e= 0, the impact is termed perfectly plastic, after which the two particles stick to move together at a common velocity; when e= 1, the impact is termed perfectly elastic, with which no energy is lost during the collision. 2.In the case of oblique impact, the velocities of the two colliding bodies before and after impact are resolved into ncomponents along the line of impact and tcomponents along the plane of contact (common tangent to the surfaces in contact). In the tdirection, ((((2,1,2,1,,tBtBtAtAvvvv==while in the ndirection, ((((2,2,1,1,nBBnAAnBBnAAvmvmvmvm+=+(((([].1,1,2,2,nBnAnAnBvvevv-=-Note: The coefficient of restitution relation is only valid along line of impact, i.e., n directionA B (vB)1with .

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