On a frictionless horizontal table,two blocks (A of mass 2.00 kg and B of mass 3.00 kg)are pressed together against an ideal massless spring that stores 75.0 J of elastic potential energy.The blocks are not attached to the spring and are free to move free of it once they are released from rest.The maximum speed achieved by each block is closest to
A) 6.71 m/s (A), 4.47 m/s (B).
B) 4.47 m/s (A), 6.71 m/s (B).
C) 5.48 m/s for both.
D) 6.12 m/s (A), 5.00 m/s (B).
E) 5.00 m/s (A), 6.12 m/s (B).

Question

Quizplus · Accepted Answer

The maximum speed of each block can be found using the conservation of energy principle. The total elastic potential energy stored in the spring is converted into the kinetic energy of the two blocks. The kinetic energy ($KE$) is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity of the block. Since the total energy is conserved, the sum of the kinetic energies of both blocks equals the initial potential energy stored in the spring, i.e., $75.0 J$.For two blocks of different masses, the block with the smaller mass (A, 2.00 kg) will achieve a higher speed than the block with the larger mass (B, 3.00 kg) because the same amount of energy results in a higher velocity for the lighter object. The correct speeds, as calculated using the conservation of energy and taking into account the mass of each block, are 6.71 m/s for block A and 4.47 m/s for block B, making option A the correct choice.

On a Frictionless Horizontal Table,two Blocks (A of Mass 2