Final answer:
The speed of the block after it leaves the spring is determined by using the conservation of energy principle, which relates the potential energy stored in the compressed spring to the kinetic energy of the block upon release.
Step-by-step explanation:
The speed of the block after it leaves the spring can be determined using the conservation of energy principle. The potential energy stored in the spring when it is compressed is converted into the kinetic energy of the block when the spring is released. The potential energy of the spring (PE_spring) is given by the formula PE_spring = (1/2) k x^2 where k is the spring constant and x is the compression distance. The kinetic energy of the block (KE_block) when it leaves the spring is given by KE_block = (1/2) m v^2 where m is the mass of the block and v is the speed of the block.
By equating the potential energy of the spring to the kinetic energy of the block, we can solve for the speed v as follows: (1/2) k x^2 = (1/2) m v^2, which simplifies to v = sqrt((k x^2)/m). Substituting in the given values k = 190 N/m, x = 2.20 x 10 m (likely meant to be 2.20 x 10^-2 m), and m = 3.70 kg, we can calculate the speed v.