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KL=Work: A Definition Work is a familiar concept. It takes work to push a heavy object such as a stalled car. In fact more work is done when the pushing force is greater or when the displacement of the car is greater. Force and displacement, then, are the two essential elements of work. The diagram below shows a constant force F of magnitude 10.0 N acting in the same direction as the displacement d of the object. The object moves 2.00 m. s s d | For the situation above, work is defined as the magnitude of the force, F, times the magnitude of the displacement, d, W = Fd. The work done to push a car is the same whether the car is moved north to south or east to west, provided that the amount of force and the distance moved are the same. Work does not have a direction, and is therefore a scalar quantity. The equation W = Fd indicates that the unit of work is the unit of force times the unit of distance, or the newton?metre in S| units. One newton-metre is referred to as a joule (J) in honour of James Joule (1818 - 1889) and his work into the nature of work, energy, and heat. For the example above, the work done is W= (10.0 N)(2.00 m) =20.0 J. We can now formally define work. The work done on an object by a constant force is W = Fd where F is the magnitude of the force, and d is the magnitude of the displacement. The SI unit of work fs the newton-metre, also referred to as the joule (J). This definition of work has a feature that may be surprising. If the displacement d is zero, then the work is zero, even if a force is applied. Pushing on an immovable object, such as a concrete wall, may tire your muscles, but there is no work done of the type we are discussing. In physics, the idea of work is intimately tied up with the idea of motion. If there is no movement of the object, the work done by the force acting on the object is zero. L=Work and Force at an Angle Often the force and the displacement do not point in the same direction. In our definition of work, it is important that the force and the magnitude of the displacement point along the same direction. If they do not, then we must determine the component of the force along the displacement. For example, suppose that a force of 10.0 N is applied at an angle of 60.0 above the horizontal and the object moves a distance of 2.00 m. _ The component of the force that is in the direction of the displacement is F cosO. Therefore the work done is W= F cos@ d = (10.0 N)( cos 60.0)(2.00 m) = 10.0 J. When the force points in the same direction as the displacement, the = 0 and the equation for work remains W = Fd. L= Positive and Negative Work Work can be either positive or negative depending on whether a component of the force points in the same direction as the displacement or in the opposite direction. If the force has a component in the same direction as the displacement of the object, the work done by the force is positive. On the other hand, if a component of the force points in the direction opposite to the displacement, the work is negative. If the force is perpendicular to the displacement, the force has no component in the direction of the displacement and the work is zero. An example could be a weight lifter bench-pressing a barbell whose weight is 710 N. When the person raises the barbell a distance of 0.60 m above the chest, the work done is W = Fd = (710 N)(0.60 m) = 426 J or 430 J When the weight is brought back down, the force the lifter is exerting is up but the weight is moving down. Since the force and the displacement are in opposite directions, the work done in the downward motion is W = -430 J. Each complete up-and-down movement of the barbell is called a repetition or "rep."\" The lifting of the weight is referred to as the positive part of the rep, and the lowering is known as the negative part of the rep. Another example would be a person pulling a mass to the right at a constant speed with a force of 10.0 N for a distance of 2.00 m. Because the mass is moving at a constant speed, the net force is zero and there must be an equal and opposite force directed to the left. This other force could be the force of friction. The work done by the person is W= Fd=(10.0 N)(2.00 m) =20.0 J The work done by the force of friction is -20.0 J because the direction of the force of friction is directly opposite the direction of the displacement. LwSummary In this lesson we learned the meaning of the term "work" and how to calculate it. The work done on an object by a constant force is W = Fd where F is the magnitude of the force, and d is the magnitude of the displacement. The Sl unit of work is the newton-metre, also referred to as the joule (J). Work does not have a direction, and is therefore a scalar quantity. In calculating work done, it is important that the force and the magnitude of the displacement point along the same direction. If they do not, then we must determine the component of the force along the displacement. If the force has a component in the same direction as the displacement of the object, the work done by the force is positive. If a component of the force points in the direction opposite to the displacement, the work is negative. If the force is perpendicular to the displacement, the force has no component in the direction of the displacement and the work is zero. These ideas will lead us into the next lesson where we will study kinetic energy and the work-energy theorem. Question(s): The physics of work and pushing a refrigerator at an angle. A 2.40 x 102 N force is pulling an 85.0 kg refrigerator across a horizontal surface. The force acts at an angle of 20.0 above the surface. The coefficient of kinetic friction is 0.200, and the refrigerator moves a distance of 8.00 m. Determine the following: 1. The work done by the pulling force. 2. A free body diagram with appropriate labels for the forces. 3. The normal force. 4. The force of friction. 5. The work done by the force of friction