Exercise #8.46): A 0.160 kg glider is moving to the right on a frictionless, hor

Question

Exercise #8.46): A 0.160 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.760 m/s. It has a head on collision with a 0.308 kg glider that is moving to the left with a speed of 2.17 m/s. Suppose collision is elastic.

Part A- Find the magnitude of the final velocity of the 0.160kg glider…

Part B- Find the direction of the velocity of the 0.160 kg glider....

Part C- Find the magnitude of the final velocity of the 0.308 kg glider...

Part D- Find the direction of the final velocity of the 0.308 kg glider...

Explanation / Answer

m1= mass of glider 1=0.160 kg
m2= mass of glider 2=0.308 kg
vi1=initial velocity of glider 1=0.760 m/s
vi2=initial velocity of glider 2=-2.17 m/s
Collision is elastic; therefore KE is conserved.

m1v1i - m2v2i = m1v1f + m2v2f
0.160*0.760 - 0.308*(-2.17) = m1v1f + m2v2f
-0.54676 = m1v1f + m2v2f
-0.54676 - 0.160v1f = 0.308v2f

1/2m1v1i^2 + 1/2m2v2i^2 = 1/2m1v1f^2 + 1/2m2v2f^2

2* [1/2*0.160*(0.760)^2 + 1/2*0.308*(2.17)^2 ] = m1v1f^2 + m2v2f^2

1.5427572 = m1v1f^2 + m2v2f^2

1.5427572 = 0.160v1f^2 + 0.308v2f^2

v1f = -3.09658 m/s to the left
v2f = -0.166581 m/s to the left

Physical intuition tells us that the lighter glider (1) will not push the heavier, faster moving glider out of the way so the “-” solution is correct.

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