Two boxes are seen to accelerate at the same rate when a force F is applied to the first and 5 F is applied the second.
What is the mass ratio of the first box to the second?
F = ma,
m1 = F/a.
5F = ma,
m2 = 5F/a.
m1/m2=(F/a) / (5F/a)=F / a * a/5F = 1/5
Why did the box apply for a restraining order against the force? Because it couldn't handle the constant acceleration!
But to answer your question, let's use Newton's second law of motion: F = ma. Since the acceleration is the same for both boxes, we can set up two equations:
For the first box: F = m1 * a
For the second box: 5F = m2 * a
Dividing the second equation by the first equation, we get:
5F / F = m2 * a / (m1 * a)
5 = m2 / m1
So, the mass ratio of the first box to the second is 1:5. The second box is five times heavier than the first one! Now that's some heavy lifting!
To determine the mass ratio of the first box to the second, we can set up an equation based on Newton's second law of motion. According to Newton's second law, the force applied to an object is equal to its mass multiplied by its acceleration.
Let's assume the mass of the first box is represented by m1, and the mass of the second box is represented by m2. The force applied to the first box is F, so its acceleration can be described as F/m1. Similarly, the force applied to the second box is 5F, so its acceleration can be described as (5F)/m2.
Since both boxes are seen to accelerate at the same rate, we can equate their accelerations:
F/m1 = (5F)/m2
To find the mass ratio, we can simplify this equation:
m2/m1 = (5F)/(F)
m2/m1 = 5/1
m2/m1 = 5
Therefore, the mass ratio of the first box to the second box is 5:1.
To find the mass ratio of the first box to the second, we can use Newton's second law of motion, which states that the force on an object is equal to the mass of the object multiplied by its acceleration.
Let's denote the mass of the first box as m1 and the mass of the second box as m2. The force applied to the first box is F, and the force applied to the second box is 5F. Since both boxes are accelerating at the same rate, their acceleration can be denoted as a for both boxes.
According to Newton's second law, we can write the following equations:
F = m1 * a ---(1)
5F = m2 * a ---(2)
We can divide equation (2) by equation (1) to eliminate the acceleration term:
5F / F = (m2 * a) / (m1 * a)
Simplifying further, we get:
5 = m2 / m1
So, the mass ratio of the first box to the second is 1:5.