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Home Minds On Work and Energy Mission WE1 Work Help Help 8

Mission WE1 Work

The Question

A man is walking through an airport with a suitcase. The man exerts a constant upward force upon the suitcase as he walks a distance of 20 meters. In this example, the man is doing ____ work upon the suitcase.

Define Help

Definition of Work:
When a force acts upon an object to cause (or to hinder) a displacement, Work is done upon the object. Mathematically, work  is the dot product of the force and displacement for such a situation.

Formula Fix

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)

Think About It

A force does work upon an object if the object moves and the force somehow directly contributes to or hinders its motion. If there is no motion, then one can be sure that there is no work. In this question, there is clearly a motion - the suitcase is moving horizontally. So the next question to ask is does this upward applied force cause the displacement, hinder the displacement or have no effect whatsoever upon the displacement.
 
Mathematically, the question as to whether a force does positive work, negative work or no work whatsoever lies in the meaning of Theta (Θ) in the work equation (see Formula Frenzy section). The angle Theta (Θ) is defined as the angle between the force vector and the displacement vector. If the angle is 90 degrees, then the force does not do work upon the object. If the angle is 0 degrees (that is, the force is in the same direction as the motion), then the force does positive work upon the object. And if the angle is 180 degrees (that is, the force is in the opposite direction of the motion), then the force does negative work upon the object. To answer this question correctly, you must determine the angle between the upward force and the horizontal displacement.

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