A 3.0-kg and a 5.0-kg box rest side-by-side on a perfectly smooth,level floor.A horizontal force of 32 N is applied to the 3.0-kg box pushing it against the 5.0-kg box,and,as a result,both boxes slide along the floor.How hard do the two boxes push against each other?
A)12 N
B)20 N
C)24 N
D)32 N
E)0 N

Question

Quizplus · Accepted Answer

The force between the two boxes is equal to the force required to accelerate the 5.0-kg box. Since both boxes move together, they have the same acceleration. The force applied to the 3.0-kg box is 32 N, which accelerates both boxes. The total mass being accelerated is 3.0 kg + 5.0 kg = 8.0 kg. The force between the boxes can be found by using Newton's second law, $F = ma$, where $F$ is the force applied to the 5.0-kg box, $m$ is its mass, and $a$ is the acceleration of both boxes. The acceleration $a$ can be found from the total force divided by the total mass, $a = \frac{32\,N}{8.0\,kg} = 4.0\,m/s^2$. The force on the 5.0-kg box (which is the same as the force they push against each other due to Newton's third law) is $F = 5.0\,kg \times 4.0\,m/s^2 = 20\,N$.

A 30-Kg and a 5