Question

two stationary objects of mass 1 kg and 2 kg are connected by a tensed and suspended from a spring. the thread is cut. immediately after the cut, what are the magnitudes of the accelerations of the objects in terms of the acceleration due to gravity g?
acceleration of 1 kg object acceleration of 2 kg object

Explanation:

Step1: Analyze forces on 1 - kg object

Before cutting, the spring exerts an upward force equal to the total weight of the two - object system, $F=(1 + 2)g=3g$. When the thread is cut, the force on the 1 - kg object is $F - mg$ (where $m = 1$ kg). Using Newton's second law $F_{net}=ma$, we have $3g-1g = 1\times a_1$.

Step2: Solve for acceleration of 1 - kg object

Simplify the equation $3g - 1g=a_1$, so $a_1 = 2g$.

Step3: Analyze forces on 2 - kg object

When the thread is cut, the only force acting on the 2 - kg object is its weight $F_{2}=2g$. Using Newton's second law $F_{net}=ma$, with $m = 2$ kg and $F_{net}=2g$, we have $2g=2\times a_2$.

Step4: Solve for acceleration of 2 - kg object

Simplify the equation $2g = 2a_2$, so $a_2=g$.

Answer:

Acceleration of 1 - kg object: $2g$, Acceleration of 2 - kg object: $g$