The spring shown in the figure is compressed 47 cm and used to launch a 100 kg p

Question

The spring shown in the figure is compressed 47 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30 degree incline is 0.13. (Figure 1) What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A)    Gain in Kinetic energy = work done by spring

=>   1/2 * 80000 * 0.47 * 0.47 = 1/2 * 100 * v2

=>     v = 13.29   m/sec                 ----------------> speed after losing contact with spring .

Part B)      For speed at bottom

=> 1/2 * 100 * v2 =    100 * 9.8 * 10 + 1/2 * 100 * 13.29 * 13.29

=>   v = 19.3 m/sec

For the incline

=>     1/2 * 100 * 19.3 * 19.3   =    0.13 * 100 * 9.8 * cos30 * x + 100 * 9.8 * sin30 * x

=>   x = 31.023 m                ------------------->   distance up the incline student go

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