A block of mass 4 kg is attached to a spring whose spring constant is k = 1.10 103 N/m. The block is free to slide on a flat frictionless surface. The block is pushed to compress the spring by 18 cm, and then released. Assume the potential energy of the spring is zero at x = 0 where the spring is neither stretched nor compressed.

(a) Find the value or values of x where the kinetic energy of the block is momentarily 15% of the total mechanical energy of the system.

(b) Find the velocity of the block when this occurs.

Guest Mar 1, 2019

#1**+3 **

Total mechanical energy: E = (1/2)Mv^{2} + (1/2)kx^{2} where M is mass, v is velocity

At 18cm, assuming we start with zero velocity, E = (1/2)*1.1*10^{3}*(0.18)^2 Joules

(a) Let xa be the value of x when the PE is 15% of E: (1/2)k*xa^{2} = 0.15*(1/2)k*(0.18)^2 or xa = sqrt(0.15)*0.18 m

(b) Let va be the velocity at this point. (1/2)*4*va^2 + (1/2)*1.1*10^{3}*xa^{2} = (1/2)*1.1*10^{3}*(0.18)^2 solve for va (in m/s)

I'll leave you to do the number crunching.

Alan Mar 1, 2019