Question

In: Physics

The spring shown in the figure is compressed 52 cm and used to launch a 100...

The spring shown in the figure is compressed 52 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 0.19 .

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.

Solutions

Expert Solution


Given

   k = 80000 N/m
   m = 100 kg,
   x = -0.52m
  

The student's coefficient of kinetic friction on the 30∘ incline is 0.19 .


by conservation of energy 1/2 kx^2 = 1/2 mv^2

               v = sqrt(kx^2/m)


               V = sqrt(80000*(-0.52)^2/100) m/s

               v 14.71 m/s


b) here considering the energies involved as


       0.5 kx^2+ mgh = mgh' + F*s

hereF is frictional force = muek*mg cos theta,h' = d sdin theta

   0.5 kx^2+ mgh = mgh' + F*s
   0.5 k x^2 + mgh = mg d sin theta + mue k*mg cos theta

substituting the values


   0.5 *80000(-0.52)^2 + 100*9.8*10 = 100*9.8*d sin 30 + 0.19*100*9.8 cos30

   d = 41.744 m


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