In a ride called \"Splash Mesa\" at Duff Gardens (a rather obvious rip-off of Di

Question

In a ride called "Splash Mesa" at Duff Gardens (a rather obvious rip-off of Disney's "Splash Mountain") you sit in a hollowed-out log that is initially accelerated by a compressed spring, slides down a ramp, then goes through a shallow pool of water before running into a bumper where the ride ends and passengers disembark. The log (with passengers) has a mass m = 800 kg. The spring that initially accelerates the log has a spring constant k = 23,000 N/m and is initially compressed by 2.0 meters relative to its rest length. The platform where the ride begins is a height h = 17 meters above the level where the ride ends and is covered in rollers that allow the log to move across it with essentially zero friction; the downhill ramp has a length L = 41 meters and is also covered with the frictionless rollers. The water pool at the bottom extends a distance d = 65 meters horizontally. The interaction of the moving log with the water can be modeled as kinetic friction with a coefficient (it = 0.35. How fast is the log moving when it reaches the end of the water, i.e., just before it is stopped by running into the bumper at the end? (Note: you must solve this problem using the Work-KE theorem If there is some other approach you also like, you are welcome to use that as an assessment.)

Explanation / Answer

at the end of the ramp

1/2mv^2 = 1/2kx^2+mgh

1/2mv^2 = 1/2*23000*2^2+800*9.8*17 = 46000+133280

v = 21.17 m/s

work done by friction = -mue*mg*d

1/2mv^2-1/2mv1^2 = -mue*mgd

v2^2-v1^2 = -2mue*gd

v2^2 = 21.17^2-0.35*9.8*2*65

v2 = 1.516 m/s

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