Asked by ashley
The two blocks of masses M and 2M shown above initially travel at the same speed v but in opposite directions. They collide and stick together. What is the final velocity of the mass M after the collision?
negative one sixth v.
negative one third v.
Zero
one sixth v.
one third v.
negative one sixth v.
negative one third v.
Zero
one sixth v.
one third v.
Answers
Answered by
Ashton
Initial momentum must equal final momentum
V = initial velocity of the blocks, v = final velocity of the two
2VM – VM = 3Mv
MV = 3Mv
v = ⅓V
initial KE = ½MV² + ½2MV² = 1.5MV²
final KE = ½3Mv²
Lost KE = 1.5MV² – ½3Mv²
substituting v = ⅓V
Lost KE = 1.5MV² – ½3M(⅓V)²
Lost KE = 1.5MV² – ½3(1/9)MV²
Lost KE = 1.5MV² – (1/6)MV²
Lost KE = 1.333MV²
and that is (d)
(D) 4/3 Mv2
V = initial velocity of the blocks, v = final velocity of the two
2VM – VM = 3Mv
MV = 3Mv
v = ⅓V
initial KE = ½MV² + ½2MV² = 1.5MV²
final KE = ½3Mv²
Lost KE = 1.5MV² – ½3Mv²
substituting v = ⅓V
Lost KE = 1.5MV² – ½3M(⅓V)²
Lost KE = 1.5MV² – ½3(1/9)MV²
Lost KE = 1.5MV² – (1/6)MV²
Lost KE = 1.333MV²
and that is (d)
(D) 4/3 Mv2
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