A spring with a force constant of 20,000 N/m is compressed by X = 0.1 m launch a

Question

A spring with a force constant of 20,000 N/m is compressed by X = 0.1 m launch a student with a mass of 50 kg at the maximum speed attainable. The track shown below is frictionless except for the final 30 degree incline, where the coefficient of kinetic friction is 0.10. Find; (a) The student's speed right after losing contact with spring (x = X)? Ans.____ (b) The student's linear momentum in the valley? Ans.____ (b) The student's linear momentum in the valley? Ans._____ (c) How far the student can go along the incline? Ans.____ (d) What is the work done by the friction force? Ans.___ (e) what is the work done by the gravitation force? Ans.____

Explanation / Answer

Apply conservation of energy

1/2 m v^2 = 1/2 k x^2

v = sqrt k x^2/m

= sqrt 20,000 ( 0.1)^2 / 50

=2 m/s

Apply kinematic equation

vf^2 - v^2 = 2gh

vf = sqrt ( 2)^2 + 2 ( 9.8) 1 m)

= 4.85 m/s

(b)

P = mvf = 50 ( 4.85) = 242.899 kg m/s

(c)

mg sin theta + fk = ma

ma = mg sin theta + uk mg cos theta

a = g sin theta + uk g cos theta

= 9.8 sin 30 + 0.1 ( 9.8) cos 30

=5.74 m/s^2

Apply kinematic equation

v ^2= sqrt 2 as

4.85 ^2 = 2 ( 5.74 ) (s)

s = 2.04 m

(d)

w= fk * s

= uk mg cos theta s

= 0.1 ( 50 ) ( 9.8) cos 30 * 2.04 m

= 86.56 J

As per guide lines I worked first four subparts

  

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