Question

Three identical 6.0-kg cubes are placed on a horizontal frictionless surface in contact with one another. The cubes are lined up from left to right and a force is applied to the left side of the left cube causing all three cubes to accelerate to the right at 2.0 m/s2 . What is the magnitude of the force exerted on the middle cube by the left cube in this case?

Answer 1

Answer:

24 N

Explanation:

$m$ = mass of the cube = $6.0 kg$

Consider the three cubes together as one.

$M$ = mass of the three cubes together = $3 m = 3 (6.0) = 18 kg$

$a$ = acceleration of the combination = 2 ms⁻²

$F$ = Force applied on the combination

Using Newton's second law

$F = ma = (18) (2) = 36 N$

$F_{L}$ = Force by the left cube on the middle cube

Consider the forces acting on left cube, from the force diagram, we have

$F - F_{L} = ma \\36 - F_{L} = (6) (2)\\F_{L} = 24 N$