students who successfully complete this primer will be able to: - identify situations that involve solving two equations and two unknowns, - Use substitution to obtain one equation and one unknown - Simplify the above result and solve for both of the unknowns Eefore working on this primer, you may want to review: - SoIVing a linear equation Figure iofl I Review v Part F - Example: Finding Two Forces (Part I) Two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force The block in (Figure t) has a mass m : 10 kg and is being pulled by a force F on a table With coefcient of static friction u, : 0.3 Four forces act on it - The applied force F (directed 9 = 30\" above the horizontal) ' The force of gravity F : mg (directly down' where g : 9.8 111/52 ), - The normal force N (directly up) ' The force of static friction f, (directly left. opposing any potential motion) if we want to find the size of the force necessary to Just barely overcome static frimion (in which case I! = #,N)' we use the condition that the sum of the forces in both directions must be 0 Using some basic trigonometry we can write this condition out for the forces in both the horizontal and vertical directions respectively as' - FcosaM,N:O - Feir19+N7mg=0 in order to find the magnitude offorce F we have to solve a system of two equations With both F and the normal force N unknown Use the methods we have learned to find an expression for F in terms of mi g: 6'. and us (no N). Express your answer in terms ofm, g, 9, and M5. V View Available Hint(s| b Hint 1. Isolating unknowns .HO-? 0 Use the subscript button to enter a subscript in your answer Review now to insert subscripts and more 9 Pearson