A collar, constrained by a sliding pin to move on a circular track, has mass m 6 6kg The circular track has a radius of R 1 9m The spring, which is connected to a pin that is fixed but can swivel, has a stiffness of k 100N m The spring's undeformed length is equal to the radius of the circular track (so the spring is in tension when the collar is at position 1) The colar is released from rest at position 1 and slides round to position 2 where 0 40 Assume negligible friction, and g 9 8m s 2 , Recall that a circular track is described with respect to a point on its edge by r 2Rcos () 8 Sliding pin and collar m k R Circular Track Fixed, swivel pin (a) What is the speed of the collar at position 2 (Assume the collar is small compared to the curvature of the track) 6 806 m s (b) What is the dr dtof the collar at position 2 (c) What is the angular velocity of the collar at position 2

Question: A collar, constrained by a sliding pin to move on a circular track, has mass m = 6.6kg. The circular track has a radius of

A collar, constrained by a sliding pin to move on a circular track, has mass m = 6.6kg.

The circular track has a radius of R = 1.9m.

The spring, which is connected to a pin that is fixed but can swivel, has a stiffness of k = 100N/m.

The spring's undeformed length is equal to the radius of the circular track (so the spring is in tension when the collar is at position 1).

The colar is released from rest at position 1 and slides round to position 2 where 0 = 40⁰.

Assume negligible friction, and g = 9.8m/s², Recall that a circular track is described with respect to a point on its edge by r = 2Rcos (θ).

8 Sliding pin and collar m k R Circular Track Fixed, swivel

8 Sliding pin and collar m k R Circular Track Fixed, swivel pin (a) What is the speed of the collar at position 2 (Assume the collar is small compared to the curvature of the track)? 6.806 m/s (b) What is the dr/ dtof the collar at position 2? (c) What is the angular velocity of the collar at position 2?

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