Understanding the Forces

* Gravity: The block experiences a downward force due to gravity, which is *mg*.

* Spring Force: The spring exerts an upward force proportional to its elongation, given by *kx*, where *x* is the elongation.

* Net Force: The net force acting on the block is the difference between the spring force and the gravitational force. Since the block is accelerating upwards, the net force must be upwards.

Applying Newton's Second Law

Newton's Second Law states that the net force on an object is equal to its mass times its acceleration:

* *F_net* = *ma*

Setting up the Equation

Let's define upwards as the positive direction. With this convention:

* *F_net* = *kx - mg*

* *a* = the given upward acceleration

Now, substituting into Newton's Second Law:

* *kx - mg* = *ma*

Solving for Elongation (x)

1. Rearrange the equation to isolate *x*:

* *kx* = *ma + mg*

* *x* = (*ma + mg*) / *k*

2. Simplify:

* *x* = *m(a + g) / k*

Therefore, the elongation of the spring is given by x = m(a + g) / k