>> Work is accomplished when a force is applied and an object moves and the amount of work can be calculated as multiplying the force times the distance. That is consider this problem. 50 pounds of vertical force on a rope lifts an object 30 feet, how much work is accomplished? Well with using this formula, work is force times distance or F times D. Here the amount of force is 50 pounds, the distance the object moves is 30 feet, 50 times 30, 1500. Notice the unit of measure here, we have pounds and feet, pounds feet, pounds feet, foot pound. Foot pounds is the unit for measuring work. Now the idea of just multiplying force times distance works out really well as long as the force applied is in the same direction as in the movement of the object and that is the case in the first problem and that is the case in this one as well. A football player uses 200 pounds of horizontal force to move a blocking sled 40 feet. Now let's think about that direction of motion here, so the 200 pounds of force is being applied horizontally, you see in the same direction as the movement of the blocking sled, the movement of the blocking sled is also horizontal. So we can just directly apply our work formula, work is force times distance, the force is 200 pounds, the distance is 40 feet. 200 times 40, 8,000; 8,000 foot pounds of work is accomplished. Now let's consider a situation where the force is not in the direction of the movement of the object. Let us suppose we have a wagon here and the force applied on the handle of the wagon is 50 pounds and the angle here between the horizontal and this handle is 60 degrees. Now the movement of the wagon, let's say the wagon moves 12 feet, now how much work is accomplished. Well it is a similar idea to the notion of force ties distance, but it is the idea that we want the force along this line. We want horizontal force, we want the force along the same direction as the movement of the object, you see. So we want a resultant force times distance. Now what about this resulting force, you see it is the resultant force right here and we have a right triangle situation and from the perspective of this 60 degree angle, we are talking about adjacent side and hypotenuse. So the cosine of 60 degrees is F over 50 cosine 60 degrees if F over 50. F then is 50 cosine 60, the cosine of 60 degrees is 1/2 so the amount of force is 25 pounds. So the amount of force you see along this in this horizontal configuration is 25 pounds and now the idea is work is 25 times 12 or 300 foot pounds. Now the situation can be sort of summarized like this, it is often the case that we have a force applied in a direction different than the movement of the object and we can kind of put the ideas together like this that the resultant force up here from right up here was calculated as some, well let me generalize it here. It was 50 cosine 60, but it was the force applied at an angle at the cosine of some angle, you see and then times distance. Well a lot of times these three factors are written as F times D, force times distance times the cosine of the angle. Okay so let's use this idea then and work another problem. Now do understand though that this works even if the force and the movement of the object are in the same direction, because if they are in the same direction, now theta is the angle between the force, the direction of the force and the direction of the movement of the object and if that angle is simply 0, we have a cosine of 0, which is 1, you see so we are back to our original formula.