A pair of blocks, one 3 times as massive as the other, are connected by a compressed spring. When the spring is released, the blocks fly apart. Compared to the heavier block, how many times faster does the lighter block accelerate?

To determine how many times faster the lighter block accelerates compared to the heavier block, we need to apply Newton's second law of motion.

Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration: F = m * a, where F is the force, m is the mass, and a is the acceleration.

Let's denote the mass of the heavier block as M and the mass of the lighter block as m. Since the heavier block is 3 times as massive as the lighter block, we have M = 3m.

Now, let's consider the forces acting on the blocks. Due to the compressed spring, a force is exerted on both blocks, causing them to accelerate in opposite directions. However, the magnitude of the force exerted on both blocks is the same, since they are connected by the same compressed spring.

Applying Newton's second law to each block individually, we have:

For the lighter block: F = m * a1,
For the heavier block: F = M * a2.

Since the magnitude of the force is the same for both blocks, we can equate the two equations:

m * a1 = M * a2.

Substituting M = 3m, we get:

m * a1 = 3m * a2.

Dividing both sides by m, we have:

a1 = 3a2.

Therefore, the acceleration of the lighter block (a1) is 3 times greater than the acceleration of the heavier block (a2). In other words, the lighter block accelerates 3 times faster than the heavier block.