![]() This article provides an explanation of work done by a variable force, its formula, and derivations. Now you can also access all the relevant study material by downloading our Vedantu app. With online classes and PDF format materials, you can stay a step ahead of others. Our teachers at Vedantu offer in-depth analysis for each topic. Thus, following this integration method for work done by a constant force is redundant. In such a calculation, pressure remains unchanged, which is why you can take it out of the equation immediately.Īfter doing this, you will arrive at an equation, whereĪs you can see, the product is the same that we would have evaluated from considering force and distance. Just as you can derive the work for a variable force using calculus, you can do the same for work done by a constant force. You know that kinetic energy change \ (K.E.) =\ĭeriving Work Done by a Constant Force with Integration We need to determine the change in kinetic energy in this equation. Calculate work done by a bullet when passing through this obstacle. This bullet strikes a windowpane and passes through it. Determine the work done when object moves from x = 0 to x = 5.Ī bullet weighing 20g is moving at a velocity of 500m/s. Force variation is a function, F x = (3 . This object undergoes variable force in direction ‘x’. Therefore,Ĭonsequently, by using this approach mentioned above, one can easily derive the work done by variable force. Integration and Formula for Variable Force Workįor work done by a variable force, however, you need to apply integration to arrive at accurate results. This force-displacement graph for spring can help in assessing force according to Hooke’s Law. U s is the elastic potential energy for a stretched spring. The figure above relates the force on the spring vs displacement when displacement is 0 for an unstretched spring. However, this spring force has an opposite direction to this extension. Hooke’s Law states that the spring force for a compressed or stretched spring is equal in magnitude to the force for extension or compression of the spring. To form a better understanding of the same, let us consider the workings of a spring. Calculating the same is quite complex and requires integration. Most of the work that we complete in our daily life is an example of variable force work. In such a case, the magnitude and direction of force can change at any time during the work. ![]() Work done by the variable force is a bit more complex. In such a case, work (W) is equal to the force applied (F) multiplied by displacement (\x). In the former kind, the magnitude and direction of the force remain unaltered. ![]() ![]() Work done by a force can be divided into work from a constant force and work from a variable force. You can complete work using a constant force or a variable force. This movement in relation to the force is defined as work. Applying force on an object causes that object to move in the direction of the force. ![]()
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