Two forces FA and FB are applied to an object whose mass is 19.0 kg. The larger force is FA. When both forces point due east, the object's acceleration has a magnitude of 1.40 m/s2. However, when FA points due east and FB points due west, the acceleration is 0.700 m/s2, due east. Find the magnitude of FA and the magnitude of FB
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To solve this problem, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Let's denote the magnitude of force FA as FA and the magnitude of force FB as FB.
In the first case where both forces point due east, we know that the object's acceleration is 1.40 m/s^2. Since only FA and FB are acting on the object, the net force can be written as:
FA - FB = mass * acceleration
FA - FB = 19.0 kg * 1.40 m/s^2
FA - FB = 26.6 N (Equation 1)
In the second case, where FA points due east and FB points due west, the object's acceleration is 0.700 m/s^2, due east. In this case, we can write the net force equation as:
FA + FB = mass * acceleration
FA + FB = 19.0 kg * 0.700 m/s^2
FA + FB = 13.3 N (Equation 2)
We now have a system of two equations with two variables (FA and FB). We can solve this system of equations by adding Equation 1 and Equation 2 to eliminate FB:
(FA - FB) + (FA + FB) = 26.6 N + 13.3 N
2FA = 39.9 N
FA = 19.95 N
Now that we have the magnitude of FA, we can substitute it back into Equation 1 to find the magnitude of FB:
19.95 N - FB = 26.6 N
FB = 19.95 N - 26.6 N
FB = -6.65 N
Since force cannot be negative, we take the magnitude of FB as:
|FB| = 6.65 N
Therefore, the magnitude of FA is 19.95 N, and the magnitude of FB is 6.65 N.