<h2>
Answer:</h2>
The acceleration of the first box (with 2.0kg mass) is 7.5m/s² in one direction and the acceleration of the second box (with 3.0kg mass) is 5.0m/s² in the opposite direction.
<h2>
Explanation:</h2><h2>
</h2>
The force (F) due to the compression (c) of the spring by both masses is given by Hooke's law as follows;
F = k x c -------------(i)
Where;
k = the spring's force constant.
From the question;
k = 250N/m
c = 6.0cm = 0.06m
<em>Substitute these values into equation (i) as follows;</em>
F = 250 x 0.06
F = 15N
This force causes both masses (boxes) to accelerate in opposite directions and the magnitude of this acceleration is given by Newton's second law of motion as follows;
F = m x a --------------(ii)
Where;
m = mass of each box
a = acceleration of each box
F = force causing the acceleration.
<em>For the first box;</em>
m = 2.0kg
<em>Substitute this value into equation (ii) as follows;</em>
F = 2.0 x a [F = 15N as calculated above]
15 = 2.0a
a =
a = 7.5m/s²
<em>For the second box;</em>
m = 3.0kg
<em>Substitute this value into equation (ii) as follows;</em>
F = 3.0 x a [F = 15N as calculated above]
15 = 3.0a
a =
a = 5.0m/s²
Therefore, the acceleration of the first box (with 2.0kg mass) is 7.5m/s² in one direction and the acceleration of the second box (with 3.0kg mass) is 5.0m/s² in the opposite direction.