PLEASE EXPLAIN STEP BY STEP! A red box and a blue box sit on a horizontal, frict

Question

PLEASE EXPLAIN STEP BY STEP!

A red box and a blue box sit on a horizontal, frictionless surface. When horizontal force F is applied to the red box, its acceleration has magnitude a = 6.71 m/s2.

a) If force F is applied to the blue box, its acceleration has magnitude a = 2.76 m/s2. Find mred/mblue, the ratio of the mass of the red box to the blue box.
1

b) Now, the two boxes are glued together. If horizontal force F is now applied to the combination, find acombo, the magnitude of the acceleration of the combination of boxes.
2 m/s2

Explanation / Answer

step1: force F is applied on red box
F = mr *6.71

step2: force F is applied on blue box

F = mb*2.76

divide the above two equations,

mr/mb =2.76/6.71

step 3 :

F = (mr+mb)*acombo

but mr = 0.4113 mb

so

F = (mb+0.4113mb)*acombo

F = 1.4113mb *a combo

now divide this with F = mb*2.76

we get a combo = 2.76/1.4113 =1.9556 m/S^2

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