EXPLORE An object of mass m1 = 15 kg and velocity 1 = -7 m/s crashes into anothe

Question

EXPLORE An object of mass m1 = 15 kg and velocity 1 = -7 m/s crashes into another object of mass m2 = 16 kg and velocity 2 = 8 m/s. The two particles stick together as a result of the collision. (A) Determine the velocity f of the objects after collision. (B) Determine the change in total mechanical energy. CONCEPTUALIZE The two particles with the masses given approach each other and then stick together, continuing their motion as if they were now one particle whose mass is the sum of the previous two masses. CATEGORIZE The problem is concerned with a collision that occurs in one dimension. The system consists of the two objects and the only forces affecting the motion are the internal forces between them during collision. ANALYZE (A) Determine the velocity after collision. Because no external force acts, the collision does not change the total momentum of the system of two particles. We set the total momentum before collision to the total momentum afterward: m1v1 + m2v2 = (m1 + m2)vf. The final velocity of the two objects joined together is given by the previous momentum conservation equation: (1) vf = m1v1 + m2v2 m1 + m2 . Using the values of this exercise, we get vf = (15 kg)(?7 m/s) + (16 kg)(8 m/s) (15 kg) + (16 kg) = .74 m/s. (B) Determine the change in total mechanical energy. While the forces that the two objects exert on each other cannot change their total momentum, they can change the total kinetic energy in an inelastic collision such as the one being considered. All of the mechanical energy in the problem is kinetic energy. The change in kinetic energy is then ?K =

Explanation / Answer

conservation of momentum 15*-7 +16*8 = (15+16)v v=0.74 m/s change in energy = KEf - KEi = 1/2*15*0.74^2 +0.5*16*0.74^2 - 0.5*15*7^2 - 0.5*16*8^2=-871 J

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