A small glider is placed against a compressed spring at the bottom of an air tra

Question

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of 45.0°above the horizontal. The glider has mass 0.0900 kg . The spring has k = 662 N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.35 m along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring.

(a) What distance was the spring originally compressed?
___ cm
(b) When the glider has traveled along the air track 0.60 m from its initial position against the compressed spring, is it still in contact with the spring?

Yes or No     

What is the kinetic energy of the glider at this point?
___J

Explanation / Answer

a)let the maximum compression point of the spring is zero potential energy point.

let maximum compression is d.

if the glider has travelled 1.35 m along the incline, height achieved=1.35*cos(45)=0.9546 m

then using conservation of energy principle:

potential energy of the spring=final potential energy of the glider

0.5*662*d^2=0.09*9.8*0.9546

==>d=0.0504 m

hence maximum compression was 5.04 cm

b)no, because maximum compression is less that the distance travelled.

c) total energy of the system at any point=0.5*662*0.0504^2=0.8408 J

let veloicty at 0.6 m distance is v.

height at this point=0.6*sin(pi/4)=0.42426 m

then kinetic energy+potential energy=total energy

==>0.5*0.09*v^2+0.09*9.8*0.42426=0.8408

==>v=3.22 m/s

then kientic energy=0.5*0.09*v^2=0.4666 J

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