Problem 9 (25 pts) Six flags has designed a crazy new kind of bumper car with sp

Question

Problem 9 (25 pts)

Six flags has designed a crazy new kind of bumper car with springs on one side and Velcro on the other (Velcro causes objects to stick together). The springs on the bumper car can be treated as one big spring with a spring constant of 700 N/m.

(A) If the bumper car 1 has a mass of 70 kg and is traveling at 4.0 m/s 15 degrees north of east and bumper car 2 has a mass of 60 kg and is traveling 25 degrees south of west when they collide on the springy side, during the collision, what is the maximum distance the springs will be compressed (assuming that both cars spring compress the same amount) (12 pts)

(A) Assuming the bumper cars have the same masses and velocities as in part (A), but this time collide with the Velcro side, find the velocity (both magnitude and direction) of the two bumper cars once they are stuck together (13 pts)

Explanation / Answer

As the orientation of the springs is not given
Using energy conservation
0.5*70*4^2 + 0.5*60*4^2 = 0.5*700*x^2*2
x = 1.12189 m

For inelastic collision
using momentum conservation
70(4(cos(15)i + sin(15)j) + 60(4(-cos(25)i - sin(25)j)) = (70+60)(v)
v = 0.407 i - 0.22 j m/s

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