Two forces F 1 and F 2 act along the two sides of an equilateral triangle as shown in Figure P11.5. Point O is the intersection of the altitudes of the triangle. (a) Find the magnitude of a third force F3 to be applied at Band along BC that will make the total torque zero about the point O. (b) What If? Will the total torque change if F 3 is applied not at B but at any other point along BC? Figure P11.5 B

Force F = (8.55 N )î – (9.95 N )ê acts on a pebble with position vector T (6.87 m )ĵ – (2.53 m )k, relative to the origin. What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (8.02 m, 0, - 6.52 m)?

F y mg f.Y Frxe f,x Axis The ladder in the picture has a mass of 32 kilograms and a length 3.2 meters. What is the normal force pushing the ladder up from the floor? FN = Assume that the ladder's weight is evenly distributed, so it can be treated as a single force through the middle. If the ladder is at a 60° angle from the ground, what is the torque exerted by the weight (using the floor as the pivot point)?

Force F = (-7.0 N)î + (5.0 N) ĵ acts on a particle with position vector7 = (4.0 m)î + (5.0 m) ĵ. (a) What is the torque on the particle about the origin, in unit-vector notation? = N: m (b) What is the angle between the directions of r and Torque is the cross product of a position vector (extending from a chosen point, here the origin, to the particle) and a force vector. Did you take the cross product in unit-vector notation? Do you remember how find the angle between two vectors by taking a dot product in both unit-vector notation and also in magnitude-angle notation? (You can similarly use a cross product to do this.) Do you remember how to find the magnitude of a vector from its components?