Answer:
7.5 m/s² and 5 m/s²
Explanation:
Note: The force in the compressed spring is the same as the force needed to produce the acceleration in each box.
From Hook's law,
F = ke..................... Equation 1
Where F = force, k = spring constant, e = compression.
Given: k = 250 N/m, e = 6.0 cm = 0.06 m
Substitute into equation 1
F = 250×0.06
F = 15 N.
Using Newton's fundamental equation of kinematics
F = ma.................. Equation 2
Where m = mass of the box, a = acceleration of the box.
make a the subject of the equation
a = F/m................. Equation 3
For the first box,
Given: m = 2.0 kg, F = 15 N
Substitute into equation 3
a = 15/2.0
a = 7.5 m/s².
For the second box,
Give: m = 3.0 kg, F = 15 N
Substitute into equation 3
a = 15/3
a = 5 m/s²
