A force applied to an object of mass m1 produces an acceleration of 3.10 m/s2. The same force applied to a second object of mass m2 produces an acceleration of 2.00 m/s2.
m1 × 3.10m/s2 = m2 × 2.00m/s2
m2 = 1.55 × m1
To find a relationship between the masses and accelerations of the two objects, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's denote the force as F, the mass of the first object as m1, the mass of the second object as m2, the acceleration of the first object as a1, and the acceleration of the second object as a2.
According to the problem, the applied force F produces an acceleration of 3.10 m/s^2 for the first object, so we have:
F = m1 * a1 (Equation 1)
Similarly, the same force F produces an acceleration of 2.00 m/s^2 for the second object, so we have:
F = m2 * a2 (Equation 2)
Now, let's divide Equation 1 by Equation 2:
(m1 * a1) / (m2 * a2) = 1
Since the force F is the same in both cases, it cancels out from the equation. Simplifying further, we get:
(m1 / m2) * (a1 / a2) = 1
This equation tells us that the ratio of the masses is equal to the inverse ratio of the accelerations.