Proportional Masses Newtons Laws

[destro47]

A red box and a blue box sit on a horizontal, frictionless surface. When horizontal force F is applied to the red box, it accelerates 4.88 m/s2.

a) If F is applied to the blue box, it accelerates at 1.32 m/s2. What is the ratio of the masses of the boxes (mass of the red box/mass of the blue box)

b) Now, the two boxes are glued together. If F is now applied to the combination, what is the acceleration of the boxes?

Got the answer to part a, turns out its .270

My question is how do we use this info to solve part b. I have a sneaking suspicion that the solution to this is the sum of the accelerations, multiplied by the ratio of the masses.


F= (m1 + m2 )[(4.88 = 1.32)(.270)]

The part in brackets is the mathematical representation of what I'm talking about here.

Let me know if I'm on the right track with this please, I only have a limited number of times to submit the answer for my physics homework.

 

[Nate810]

Yes, you are on the right track. The acceleration of the combination is the sum of the accelerations of the individual boxes multiplied by their ratio of masses. So, the acceleration of the combination is given by:a = (4.88 + 1.32) × 0.270 = 2.06 m/s2

 

[Moetasim]

Yes, you are on the right track with your thinking! To solve part b, we can use Newton's Second Law, which states that the net force on an object is equal to its mass multiplied by its acceleration (F=ma).

In this case, we have a combined mass of the two boxes (m1 + m2) and we know that the net force acting on them is still F. So, we can set up the following equation:

F = (m1 + m2) * a

Since we already know the ratio of the masses from part a, we can substitute that into the equation:

F = (m1 + m2) * (4.88/1.32) * a

Now, we can solve for the acceleration (a):

a = F / (m1 + m2) * (4.88/1.32)

This gives us the acceleration of the combined boxes when the force F is applied. We can also simplify this equation to:

a = (4.88/1.32) * (F / (m1 + m2))

So, the acceleration of the combined boxes is equal to the ratio of the accelerations from part a, multiplied by the force F, divided by the combined mass of the boxes.

I hope this helps and good luck with your physics homework!