A 2 kg collar is attached to a spring and slides without friction in a vertical

Question

A 2 kg collar is attached to a spring and slides without friction in a vertical plane along the curved rod

ABC. The spring is un-deformed when the collar is at C and its constant is 600 N/m. If the collar is

released at A with no initial velocity, determine its velocity:

a) As it passes through B

b) As it reaches C

A 2 kg collar is attached to a spring and slides without friction in a vertical plane along the curved rod ABC. The spring is un-deformed when the collar is at C and its constant is 600 N/m. If the collar is released at A with no initial velocity, determine its velocity: As it passes through B As it reaches C

Explanation / Answer

At A extension in spring=0.25-0.15=0.1 m

So

Conserving energy from A to B we have

E(spring (A)) +E(gravitational pot.) = E(Kinetic)+E(spring(B))

1/2*600*0.1^2+2*9.8*0.2=1/2*2*v^2+1/2*600*0.05^2

So

v=2.484m/s (at B)

Conserving energy from A to C we have

E(spring (A)) = E(Kinetic)+E(spring(C)) (no gravity pot. as both at same height)

1/2*600*0.1^2 = 1/2*2*v^2 + 0

So

v=1.732m/s (at C)

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