please show all work with formulas. this involves calculus. (30 points) A. Calcu

Question

please show all work with formulas. this involves calculus.

(30 points) A. Calculate the final velocity of two masses on a frictionless air track, moving toward each other, with the following data. The two masses collide and stick together during the collision. 2. M1 3.35 kg moving to the right at 2.4 m/s M2 5.46 kg moving to the left at 1.5 m/s VA m/s Direction: (circle one) right; or left B. How much kinetic energy is lost (if any) in the collision? C. What type of collision is this? Circle one: completely elastic; elastic; inelastic; or completely inelastic.

Explanation / Answer

2. Applying momentum conservation,

pi = pf

(3.35 x 2.4) + (5.46 x -1.5) = (3.35 + 5.46) v

v = - 0.017 m/s

Ans: vA = 0.017 m/s

direction = left  

(B) Ki = (3.35 x 2.4^2 / 2) + (5.46 x 1.5^2 / 2) = 15.7905 J  

Kf = (3.35 + 5.46)(0.017^2)/2 = 1.273 x 10^-3 J  

K_lost = Ki- Kf = 15.8 J

(C) both mass moves together.

velocity of separation = 0

Ans: Completely inelastic

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