A horizontal spring attached to a wall has a force constant of k = 850 N/m. A bl

Question

A horizontal spring attached to a wall has a force constant of k = 850 N/m. A block of mass m = 1.00 kg is attached to the spring and rests on a frictionless, horizontal surface.
a) The block is pulled to a position x = 6 cm from equilibrium and released. Find the elastic potential energy stored in the spring when the block is 6 cm from equilibrium and when the block passes through equilibrium.

b) Find the speed of the block as it passes through the equilibrium point.

c) What is the speed of the block when it is at a position x(initial)/2 = 3 cm?

d) Why isn't the answer to part c half the answer to part b?

Explanation / Answer

The mass of the block is m = 1 kg The force constant of the spring is k = 850 N/m a) The distance of the block from equilibrium, x = 6 cm The elastic potential energy of the spring is given by, U = kx^2 U = (850 N/m)*(0.06 m)^2 U = 3.06 J When the block is passed through the equilibrium, at equilibrium, the energy of the block is only kinetic energy which is equal to the elestic potential energy of the spring, when the block is at extreme, according to the conservation of energy. E = 3.06 J b) As the block has only kinetic energy at the equilibrium, 0.5*m*v^2 = 3.06 J v = 2.5 m/s c) The accelertation of the block is given by a = (v^2 - u^2)/2x a = [6.25 m^2/s^2] / 2*(0.06) a = 52.08 m/s^2 The speed of the block at 3 cm from the extreme is v^2-u^2 = 2ax v^2 = 2*52.08 m/s^2 * 0.03 m v = 1.77 m/s d) The answer to part c half the answer to part b because, the block is not moving with a constant speed as it has a non-zero acceleration.

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