A block of mass m is attached to a massless spring of spring constant k. This system is accelerated upward with acceleration a. The elongation in spring will be?

Question

Answer

Analysis:
The motion of the block attached to the spring can be analyzed using Newton's second law and the spring force.

Newton's Second Law:
The net force acting on the block is given by:
$$ F_{\text{net}} = ma $$

Spring Force:
The spring force is given by Hooke's Law:
$$ F_{\text{spring}} = -kx $$
where x is the elongation in the spring.

Equilibrium of Forces:
At equilibrium, the net force is zero:
$$ ma = kx $$
Solving for x, we get:
$$ x = \frac{ma}{k} $$
Therefore, the elongation in the spring when the system is accelerated upward with acceleration a is $$ \frac{ma}{k} $$.

Answer

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