Two forces are applied to an object with mass m = 5.25 kg and the resulting acceleration is ay = 2.09 m/s2 in the positive y direction with no acceleration in the x direction. One of the two forces being applied to the object is F2 = 14.7 N acting in the positive x direction.

Write an expression for the magnitude F1 of the other force in terms of m, F2, and ay.
What is F1 in N?

F = ma, so

(14.7,0) + (Fx,Fy) = (0,2.9*5.25)
F = (-14.7,15.225)

Well, if we know that the object has no acceleration in the x direction, we can assume that the net force in that direction is zero. And since we know that one of the forces acting on the object is F2 = 14.7 N in the positive x direction, the other force must be equal in magnitude but in the opposite direction.

So, the expression for the magnitude of the other force, F1, can be written as:
F1 = -F2

Plugging in the values, we have:
F1 = -14.7 N

And since we want the magnitude of F1, we just take the absolute value, which gives us:
|F1| = |-14.7 N| = 14.7 N

Therefore, F1 is 14.7 N.

To find the magnitude of the other force F1, we can use Newton's second law of motion, which states that the net force applied to an object is equal to the product of its mass and acceleration:

F_net = m * a

Since there is no acceleration in the x direction, the net force in the x direction must be zero. Therefore, the sum of the forces in the x direction must be zero:

F1 + F2 = 0

Solving for F1, we have:

F1 = -F2

Substituting the given value for F2 (F2 = 14.7 N), we can find F1:

F1 = -14.7 N

Note that the negative sign indicates that the force F1 is in the opposite direction of F2.

To find the magnitude of the other force, F1, in terms of mass (m), F2, and acceleration in the y direction (ay), you can use Newton's second law of motion.

Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration. In equation form, it can be written as:

Fnet = m * a

In this case, the acceleration in the x direction is zero, so the net force in the x direction is also zero. Therefore, we can write:

F1 + F2 = 0

Since F2 is given in the problem as 14.7 N, we can substitute that into the equation:

F1 + 14.7 N = 0

Now, we can isolate F1 by rearranging the equation:

F1 = -14.7 N

Therefore, the expression for the magnitude F1 of the other force in terms of m, F2, and ay is F1 = -14.7 N.

As for the second part of the question, F1 is equal to -14.7 N. However, the negative sign indicates that the force is in the opposite direction of the positive x-axis. If you are looking for the magnitude of the force, simply ignore the negative sign. Therefore, the magnitude of F1 is 14.7 N.