Amount of Kinetic Energy Lost in Inelastic Collision

AI Thread Summary
In an inelastic collision between two carts of mass M, one moving at velocity V and the other at -3V, the initial kinetic energy (KE) is calculated as 10mv². After the collision, where momentum is conserved, the combined velocity of the two carts is -V, resulting in a final KE of mv². The kinetic energy lost during the collision is determined by subtracting the final KE from the initial KE, yielding a loss of 9mv². However, a correction reveals that the actual loss is 4mv² due to an arithmetic error in the initial calculation. The discussion emphasizes the importance of careful calculations in physics problems.
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1. Two carts, each of mass M, travel towards each other on a frictionless air track, one with velocity V, and the other with -3V. They collide and stick together. How much kinetic energy is lost in the collision?

2. P = mv, KE=1/2mv2

3. Initial KE of the system is the sum of the kinetic energies of the two masses.

K1 = (1/2)Mv2, K2 = (1/2)m(-3v)2 = 9mv2

sum: 10mv2

assuming momentum is conserved, velocity of the two masses after the collision is -V.

Then calculate final KE = 1/2(2m)(-V)2 = mv2

subtract this from the initial and I get 9mv2 Joules are lost in the collision.

My key says the answer is 4mv2
 
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K1 = (1/2)Mv2, K2 = (1/2)m(-3v)2 = 9mv2

sum: 10mv2

check your arithmetic.
 
forgot to divide by 2... goodness. Thanks!
 

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