Proportional Masses Newtons Laws

In summary, the ratio of the masses of the red box to the blue box is 0.270. When the two boxes are glued together and a horizontal force F is applied, the acceleration of the combination is 2.06 m/s2, which is equal to the sum of the individual accelerations multiplied by the ratio of masses.
  • #1
destro47
16
0
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.
 
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  • #2
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
 
  • #3


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!
 

Related to Proportional Masses Newtons Laws

1. What are the three laws of motion proposed by Newton?

The three laws of motion proposed by Newton are:

  • First Law: An object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity, unless acted upon by an external force.
  • Second Law: The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.
  • Third Law: For every action, there is an equal and opposite reaction.

2. How are mass and acceleration related according to Newton's Second Law?

According to Newton's Second Law, mass and acceleration are inversely proportional. This means that as the mass of an object increases, its acceleration decreases, and vice versa. This can be mathematically represented by the formula: F = ma, where F is the net force applied to an object, m is its mass, and a is its acceleration.

3. How does mass affect the amount of force needed to accelerate an object?

The greater the mass of an object, the more force is needed to accelerate it. This is because according to Newton's Second Law, the acceleration of an object is directly proportional to the net force applied to it. Therefore, a larger mass requires a greater force to achieve the same acceleration as a smaller mass.

4. What is the relationship between mass and inertia?

Inertia is the tendency of an object to resist changes in its state of motion. According to Newton's First Law, an object at rest will remain at rest unless acted upon by an external force. This means that the more mass an object has, the more inertia it has. Therefore, objects with greater mass require more force to change their state of motion.

5. How does the concept of proportional masses apply to Newton's Third Law?

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when two objects interact with each other, the forces they exert on each other are equal in magnitude but opposite in direction. This also applies to the masses of the objects, as the greater the mass of one object, the greater the force it will exert on the other object, and vice versa.

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