Article: Above, we dealt with work problems in which the object is moving in the same direction as the force being applied to it. In reality, this isn't always the case. In cases where the force and the object's motion are in two different directions, the difference between these two directions must also be factored into the equation for an accurate result. To begin, find the magnitude of the force and the object's displacement as you normally would. Let's look at another example problem. In this case, let's say that we're pulling a toy train forward as in the example problem above, but that this time we're actually pulling upward at a diagonal angle. In the next step, we'll take this into account, but for now, we'll stick to the basics: the train's displacement and the magnitude of the force acting on it. For our purposes, let's say that the force has a magnitude of 10 newtons and that it's moved the same 2 meters (6.6 ft) forward as before. Unlike in the examples above, with a force that's in a different direction than the object's motion, it's necessary to find the difference between these two directions in the form of the angle between them. If this information isn't provided to you, you may need to measure it yourself or deduce it from other information in the problem. In our example problem, let's say that the force is being applied about 60o above the horizontal. If the train is still moving directly forward (that is, horizontally), the angle between the force vector and the train's motion is 60o. Once you know the object's displacement, the magnitude of the force acting on it, and the angle between the force vector and its motion, solving is almost as easy as it is without having to take the angle into account. Simply take the cosine of the angle (this may require a scientific calculator) and multiply it by force and displacement to find your answer in joules. Let's solve our example problem. Using a calculator, we find that the cosine of 60o is 1/2. Plugging this into the formula, we can solve as follows: 10 newtons × 2 meters (6.6 ft) × 1/2 = 10 joules.

What is a summary?
Find the force and displacement as normal. Find the angle between the force vector and the displacement. Multiply Force × Distance × Cosine(θ).