An object, of mass m = 2 kg, is located between two massless springs on a fricti

Question

An object, of mass m = 2 kg, is located between two massless springs on a frictionless incline of 30o . Initially the object is held at a position where the lower spring (k1= 950 N/m) and upper spring (k2= 1050 N/m), are compressed and stretched, respectively, by the same length x = 0.1 m. After the object is released:

1) Determine the speed of the object when it passes by the unstretched position (x =0) of the two springs?

2) Determine the maximum compression of the upper spring when the object reaches its highest position?

Explanation / Answer

a. energy conservation at no stratch x = 0 so no springpotential initial potential + kinetic = final potential + kinetic 1/2 * 950 * 0.1^2 + 1/2 * 1050 * 0.1^2 = 2* 9.8 * 0.1 sin 30 + 1/2 * 2 * v^2 v = 3 m/s b. for max stretch final velo 0 again initial potential + kinetic = final potential + kinetic 1/2 * 950 * 0.1^2 + 1/2 * 1050 * 0.1^2 = 1/2 * 950 * x^2 + 1/2 * 1050 * x^2 + 2 * 9.8 * (0.1 + x) sin 30 solving quadretic 1000 x2 + 9.8 x - 9.02 = 0 we get x = 0.0902 m

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