Final answer:
To find the speed of the block immediately after it is released by the spring, we use the conservation of energy principle where the potential energy stored in the compressed spring is converted into the kinetic energy of the block.
Step-by-step explanation:
The question pertains to calculating the speed of a block immediately after it is released from a compressed spring. We'll be using the conservation of energy principle for this calculation. When the spring is compressed, it stores potential energy which is then converted entirely into kinetic energy when the block is released, given there's no friction or other forces doing work on the system.
Finding the Potential Energy in the Spring
Initially, the potential energy stored in the spring (spring potential energy) when the block is released can be calculated using the formula:
PEspring = (1/2)kx2
Where k is the spring constant and x is the compression distance.
Converting Potential Energy to Kinetic Energy
According to the conservation of energy, the potential energy in the spring will be converted to kinetic energy (KE) of the block when it's released:
KE = (1/2)mv2 = PEspring
Where m is the mass of the block and v is the speed of the block.
Finally, to find the speed of the block, we solve the equation for v:
v = sqrt((2PEspring) / m)
This calculation gives the speed of the block immediately after it is released from the spring.