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Mathematically, work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d) that the force causes, and the angle (Θ) between the force and displacement vectors. The formula is
W = F • d • cosine(Θ)
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This is an example of a question in which much extraneous information is provided. To accurately determine the work (W) done upon the cart, you must know the force (F), the displacement (d) and the angle (Theta) between the force vector and the displacement vector. See Formula Frenzy section. The force is the force used to pull the cart up the incline - stated in the question. The displacement is the amount of distance that the cart was moved along the incline - stated in the problem. The angle Theta (Θ) is the angle between the direction of the force and the direction of the displacement. If the object is moved in the same direction that the force acts, then this angle is 0 degrees.
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Don't be fooled by the meaning of the angle Theta (Θ)! This angle is not just any old angle. It is defined as the angle between the F and d vectors. Many students will impulsively use 30 degrees as the angle Theta (Θ) in the equation because it is the only angle that is stated. Often times, the angle Theta (Θ) is not stated, but implied. Information about the direction of the force and the displacement vectors are given so that Theta (Θ) can be determined. In this question, the force is in the same direction as the displacement - up the inclined plane. When these two vectors are in the same direction, the angle Theta (Θ) is 0 degrees.
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