Finding expression for magnitude with forces

Question

Two forces are applied to an object with mass m = 5.25 kg and the resulting acceleration is a_y = 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?

Answer 1

Given

W = 5.25 * 9.81 = 51.5 N

ay = 2.09 m/s^2

F2 = 14.7 N

Find

F1=?

Solution 

Sum Fy = may

-W + F1y = may

F1y = W + may

F1y = mg + may

F1y = m (g+ ay)

Sum Fx = 0 (no acceleration in the X)

-F1x + F2 =0

F1x = F2

 Magnitude

F1 = (F1x^2 + F1y)^1/2

F1 = (F2^2 + (m(g+ay))^2)^1/2

Sub in your variables to get your F1...