 Object is in Equilibrium when F net = 0 ◦ Either motionless or constant velocity ◦ Can also occur when resultant of 3 or more forces equals a net force of 0

 Suppose two forces are exerted on an object and sum is not zero. ◦ Find third force ◦ Equilibriant: Force that produces an equilibrium

 A 168 N sign is supported in a motionless position by two ropes that each make an angle of 22.5 o with the horizontal. What is the tension on the ropes?  Known: ◦ θ = 22.5 o ◦ Fg = 168 N  Unknown: ◦ F A = ? ◦ F B = ?

 Horizontal Component  F net,x = O, thus –F Ax + F Bx = 0  -F Acos θ + F Bcos θ = 0  F A = F B  Vertical Component  F net,y = 0, thus F Ay + F By – F g = 0  F Asin θ + F Bsin θ – F g = 0  2 F Asin θ = F g  F A = F g / (2 sin 22.5 o )  F A = 2.20x10 2 N

 Sign from previous example is now hung from an angle of 42 o with the horizontal. What force does each exert?

 Gravitational Force direction towards center of earth  But on a slant, there is a normal perpendicular force to the hill, and forces of friction parallel to the hill

 Set up a coordinate system  Find the x and y components of force for these problems  A trunk weighing 562 N is resting on a plane on an incline of 30.0 o above the horizontal. Find the components parallel and perpendicular to the plane

 F gx = -F g sin θ  F gx = -(562 N) sin 30.0 o  F gx = -281 N  F gy = -F g cos θ  F gy = -(562 N) cos 30.0 o  F gy = -487 N

 A 62 kg person on skis is going down hill sloped at 37 o. The µk between ski and snow is How fast is skier going after 5.0 sec starting from rest?  Hints ◦ Establish Coordinate system ◦ Free body diagram  Known ◦ m = 62 kgk = 0.15t = 5.0 s θ = 37 o v I = 0.0 m/s  Unknown ◦ a = ?? ◦ v = ??