Two forces FA and FB are applied to an object whose mass is 9.53 kg. The larger force is FA. When both forces point due east, the object's acceleration has a magnitude of 1.43 m/s2. However, when FA points due east and FB points due west, the acceleration is 1.28 m/s2, due east. Find (a) the magnitude of FA and (b) the magnitude of FB.
0.50 × 8
0.40 x 8
To find the magnitude of FA and FB, 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 break down the problem and solve it step by step.
Step 1: Determine the mass of the object.
The mass of the object is given as 9.53 kg.
Step 2: Calculate the net force when the forces are both pointing due east.
When both forces point due east, the net force applied to the object is the vector sum of FA and FB. Since the object is accelerating, the net force can be calculated using the formula: F_net = m * a, where F_net is the net force, m is the mass of the object, and a is the acceleration.
Using this formula, we get:
F_net = mass * acceleration
F_net = 9.53 kg * 1.43 m/s^2 = 13.6279 N
Step 3: Determine the magnitude of FA.
Since FA is the larger force, it contributes more to the net force. Therefore, we can say that:
FA - FB = F_net
Substituting the values we have, we get:
FA - FB = 13.6279 N
Step 4: Calculate the net force when FA points east and FB points west.
When FA points due east and FB points due west, the forces are in opposite directions. To calculate the net force in this case, we subtract the magnitude of the smaller force from the magnitude of the larger force.
FA - (-FB) = F_net
Simplifying and substituting the values we have, we get:
FA + FB = 13.6279 N
Step 5: Solve the system of equations.
We now have two equations:
FA - FB = 13.6279 N
FA + FB = 13.6279 N
To find the magnitudes of FA and FB, we can solve this system of equations. Adding these two equations together allows us to eliminate FB:
(FA - FB) + (FA + FB) = 13.6279 N + 13.6279 N
2FA = 27.2558 N
FA = 27.2558 N / 2
FA = 13.628 N
Substituting the value of FA into one of the equations, we can find FB:
FA + FB = 13.6279 N
13.628 N + FB = 13.6279 N
FB = 13.6279 N - 13.628 N
FB = -0.0009 N (FB points in the opposite direction of FA, so it has a negative magnitude)
Therefore, the magnitude of FA is 13.628 N and the magnitude of FB is 0.0009 N.