For example: Calculate the net force of an object weighing 20 N sitting on a table being pushed towards the right with 5 N of force, but staying still because of a friction force of 5 N.
If you are working with multiple force diagrams, make sure you keep the directions consistent throughout. Label the magnitude of each force with a “+” or “-“ sign based on the direction of the arrow you’ve drawn on the force diagram. For example: The force of gravity is a downward force making it negative. The normal force is upward making it positive. The push force is to the right making it positive, while the friction force acts to oppose this force towards the left (negative).
A standard way to label forces is with a capital F and a subscript of first letter of the force. For example, if there is a force due to friction, label it Ff. Force due to gravity: Fg = -20 N Normal force: Fn = +20 N Friction force: Ff = -5 N Push force: Fp = +5 N
For example: Fnet = Fg + Fn + Ff + Fp = -20 + 20 -5 + 5 = 0 N. Because the net force is 0 N, the object is stationary.
Draw the force diagram including the angle of the diagonal force. Sketch each arrow in the proper direction the force is acting and label it with the proper magnitude. For example: Sketch the diagram for a 10 N object experiencing a 25 N force up and to the right at an angle of 45°. There is also a friction force to the left of 10 N. Forces include: Fg = -10 N, Fn = + 10 N, Fp = 25 N, Ff = -10 N.
Remember, CAH: cosine(θ) = adjacent/hypotenuse. Fx = cos θ * F = cos(45°) * 25 = 17. 68 N. Remember, SOH: sine(θ) = opposite/hypotenuse. Fy = sin θ * F = sin(45°) * 25 = 17. 68 N. Note that there may be multiple diagonal forces acting on an object simultaneously, so you’ll have to find Fx and Fy of each force in the problem. Then sum the Fx values to obtain the total force in the horizontal direction and sum the Fy values for the total force in the vertical direction.
For example, instead of one diagonal force, the diagram will now have one vertical force pointing up with a magnitude of 17. 68 N and one horizontal force pointing to the right with a magnitude of 17. 68 N.
For example: Horizontal vectors are all forces along the x axis: Fnetx = 17. 68 – 10 = 7. 68 N. Vertical vectors are all forces along the y axis: Fnety = 17. 68 + 10 - 10 = 17. 68 N.
For example: Fnetx = 7. 68 N and Fnety = 17. 68 N Plug into equation: Fnet = √ (Fnetx2 + Fnety2) = √ (7. 682 + 17. 682) Solve: Fnet = √ (7. 682 + 17. 682) = √(58. 98 + 35. 36) = √94. 34 = 9. 71 N. The magnitude of force is 9. 71 N in a diagonal up and to the right.
