The spring shown in the figure is compressed 41 cm and used to launch a 100 kg p

Question

The spring shown in the figure is compressed 41 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 incline is 0.14 . (Figure 1) k=80,000 N/m Part A 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 Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units.

https://session.masteringphysics.com/problemAsset/1383427/7/knight_Figure_11_54.jpg

Explanation / Answer

Let the initial velocity be V.

1/2 mv^2=1/2 kx^2

1/2 (100)v^2=1/2 (80000)(0.41)^2

V=11.60 m/s

Let the speed of student at bottom most point be V1.

1/2(100) V^2=1/2(100) (11.60)^2 +(100)(9.8)(10)

V1=18.18 m/s

Let he goes L m up the incline.

Height= L sin 30=L/2

Again equating work done and energy

1/2 (100)(18.18)^2= 100(9.8)(L/2)+ (0.14)(100)(9.8)cos 30 L

165.26=17.02 L

L=9.71 m

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