Two forces and are applied to an object whose mass is 13.2 kg. The larger force is . When both forces point due east, the object's acceleration has a magnitude of 0.627 m/s2. However, when points due east and points due west, the acceleration is 0.344 m/s2, due east. Find (a) the magnitude of and (b) the magnitude of .

To solve this problem, we'll 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:

F_net = m * a

Here, we are given that the object's mass (m) is 13.2 kg, and its acceleration (a) is 0.627 m/s^2 when both forces point due east.

Let's first find the net force when both forces point due east. Since the forces are in the same direction, we'll add them to calculate the net force:

F_net = F1 + F2

Given that the larger force (F2) is and the smaller force (F1) is unknown, we can substitute these values into the equation:

F1 + F2 = m * a

Since we know the values of F2 and m, we can solve for F1:

F1 + = (13.2 kg) * (0.627 m/s^2)

Now, let's find the net force when points due east and points due west. Since the forces are in opposite directions, we'll subtract the smaller force (F1) from the larger force (F2) to calculate the net force:

F_net = F2 - F1

Given that the acceleration is in the same direction as the larger force, we'll add the acceleration to the net force equation:

F2 - F1 = m * a

Substituting the values into the equation:

- F1 = (13.2 kg) * (0.344 m/s^2)

Now, we have two equations with two unknowns (F1 and F2). We can solve this system of equations to find the values.

From the first equation, we have:

F1 + = 8.2674 kg*m/s^2

From the second equation, we have:

- F1 = 4.5168 kg*m/s^2

Now, we can solve for F1 and F2 by adding the two equations:

F1 + - F1 = 8.2674 kg*m/s^2 + 4.5168 kg*m/s^2

Simplifying the equation:

= 12.7842 kg*m/s^2

Therefore, the magnitude of the smaller force (F1) is 12.7842 kg*m/s^2.

Finally, we can find the magnitude of the larger force (F2) by substituting the value of F1 into the first equation:

F1 + F2 = (13.2 kg) * (0.627 m/s^2)

12.7842 kg*m/s^2 + F2 = 8.2744 kg*m/s^2

Subtracting 12.7842 kg*m/s^2 from both sides:

F2 = 8.2744 kg*m/s^2 - 12.7842 kg*m/s^2

Simplifying the equation:

F2 = -4.5098 kg*m/s^2

Therefore, the magnitude of the larger force (F2) is 4.5098 kg*m/s^2.