Balls Spheres
Posted in Uncategorized on 06/07/2011 05:10 am by admin
Two equal spheres of mass m is suspended by vertical ropes so that they are in contact with their centers?
the same level. A third ball of mass 2m and the same size falls vertically from height h and strikes both spheres simultaneously so that their centers makes an impact equilateral triangle in a plane veticle. (Coefficient of restitution is e) (a) Find the speeds of the spheres just after impact (b) Find the tension jerk on the ropes
Some definitions. V = velocity of the third sphere U = velocity before impact of the third sphere, after e impact = U / V such that U = KE e * V (before) = (1 / 2) 2m * V ^ 2 = m * V ^ 2 KE (after) = (1 / 2) 2m ^ U * 2 * M = (V * e) ^ 2 Change in kinetic energy = m * V ^ 2 – m * (V * e) ^ 2 = m * V ^ 2 [1 - e ^ 2] (a) If we assume that no energy n ' is lost in the collision and conservation of energy tells us that the KE lost by the third ball to be acquired by the other two. Since the collision is symmetric compared with two bullets, twice the kinetic energy will equal the change in KE of the third. KE = 2 * m * V ^ 2 [1 - E ^ 2] Let W be the velocities of two balls that are hit after the impact, then: 2 * (1 / 2) W * m ^ 2 = m * V ^ 2 [1 - E ^ 2] ^ W ^ 2 = V 2 [1 - e ^ 2] W = V * SQRT (1 – e ^ 2) (b) Impulse is the change in dynamics. Since the strings are vertical, we need to calculate the vertical component in Change the target ball movement. They each start with 0 velocity and end with W if (change of momentum) = m * m * V = W * SQRT (1 – 2 ^ e) But it is at an angle off the veritcal and we need the component in the vertical plane. Since the balls are all the same size in the corners the triangle formed by the centers at the time of impact will all be 60 degrees. The direction of impact is half this or 30 degrees (symmetry). Impulse cos = * (Change of pace) (30) Impulse = m * V * SQRT (1 – e ^ 2) * cos (30)
Balls Spheres Material
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