Question

A 2 kg collar M is attached to a spring and slides without friction in a vertical plane along the curved rod ABC as shown in figure. The spring has an un-deformed length of 100 mm and its stiffness k = 800N/m. If the collar is released from rest at A, determine its velocity

1. as it passes through B.
2. as it reaches C.

Answer 1

It passes through B (A to B)

x₁ = 250 − 100 = 150mm = 0.15

x₂ = 200 − 100 = 100mm = 0.1

W . D = ΔK . E

`1/2 K(x_1^2 - x_2^2) + mgh = 1/2m(V_2^2 - V_1^2)`

`1/2 xx 800(0.15^2 - 0.1^2) + 2 xx 9.81 xx 0.2 = 1/2 xx 2 xx (V_2^2 - 0)`

V₂ = 2.98m/s

It passes through C (A to C)

x₁ = 250 − 100 = 150mm = 0.15

x₂ = 150 − 100 = 50mm = 0.05m

W . D = ΔKE

`1/2 K(x_1^2 - x_2^2) + mgh = 1/2m(V_2^2 - V_1^2)`

`1/2 xx 800(0.15^2 - 0.05^2) = 1/2 xx 2 xx (V_2^2 - 0)`

V₂ = 2.83m/s

Velocity of collar as it passes through B = 2.98 m/s

Velocity of collar as it passes through C = 2.83 m/s