Net force F causes mass m1 to accelerate at rate a. A net force of 3F causes mass m2 to accelerate at rate 2a. What is the ratio of mass m1 to mass m2?
2/3
2:3 for ratio.
2:3
Well, well, well! It looks like we have a bit of an acceleration race going on here! Let's see if I can get to the bottom of this for you.
We start off with one force, F, causing mass m1 to accelerate at rate a. Then, we have a whopping 3F causing mass m2 to accelerate at rate 2a.
So, to find the ratio of m1 to m2, let's get mathematical, shall we? Since force is directly proportional to mass times acceleration (F = ma), we can set up an equation for each mass:
For m1: F = m1a
And for m2: 3F = m2(2a)
Now, let's play around with these equations a bit. We could rearrange the equation for m1 to solve for m1 equal to F divided by a.
Now, let's substitute that into the second equation:
3F = (F/a) * (2a)
Simplify, simplify, simplify:
3F = 2F
Well, isn't this interesting? It looks like F cancels out on both sides! Which means...
3 = 2
Uh-oh! It seems we've reached a bit of a problem. Mathematically speaking, there is no way to have a ratio of 3 to 2 between mass m1 and mass m2 based on the given information.
Looks like we're caught in a bit of a gravitational paradox here! I hope this at least gave you a laugh.
To determine the ratio of mass m1 to mass m2, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
Given that a net force F causes mass m1 to accelerate at rate a, we can write the equation as F = m1a. Similarly, a net force of 3F causes mass m2 to accelerate at rate 2a, so we can write this equation as 3F = m2(2a).
Since both equations are equal to the force and mass multiplied by acceleration, we can set them equal to each other:
m1a = m2(2a)
Simplifying the equation, we cancel out the acceleration (a) term from both sides:
m1 = 2m2
Therefore, the ratio of mass m1 to mass m2 is 2:1.
3f/f=m1*a/m2*2a
m1/m2=3/2