With explanations please! 3. A railroad car of mass m moving at v collides compl

Question

With explanations please!

3. A railroad car of mass m moving at v collides completely inelastically with a stationary railroad car of mass 3m and couples to it. How fast are they moving after the collision? a) V/4 d) 2v/3 e) 3v/4 b) V/3 c) v/2 4. A railroad car of mass m and velocity v collides completely inelastically with another stationary railroad car of mass 3m and couples to it. What fraction of the initial kinetic energy is still retained by the cars after the collision? e) 3/4 b) 1/3 d) 2/3 a) 1/4 c) 1/2

Explanation / Answer

(3) P conservation

m1u1 + m2u2 = MV

mv + 0 = (m + 3m) V

mv = 4m V

V = v/4 (option a)

(4) initial KE = 1/2 mu1^2 + 1/2 3mu2^2 = 1/2 m v^2 + 0 = 1/2 mv^2

Final KE = 1/2 (m + 3m) V^2 = 1/2 4m (v/4)^2 = 1/2 m v^2/4 = 1/8 mv^2

Fraction = final / initial = (1/8) / (1/2) = 1/4 (option a)

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