![]() ![]() For example, in Newton’s Laws of Motion, we found the speed of an object sliding down a frictionless plane by solving Newton’s second law for the acceleration and using kinematic equations for constant acceleration, obtainingį ave = 1 2 m v 2 Δ s stop = 1 2 ( 2.6 × 10 −3 kg ) ( 335 m/s ) 2 0.152 m = 960 N. The importance of the work-energy theorem, and the further generalizations to which it leads, is that it makes some types of calculations much simpler to accomplish than they would be by trying to solve Newton’s second law. If you leave out any forces that act on an object, or if you include any forces that don’t act on it, you will get a wrong result. When calculating the net work, you must include all the forces that act on an object. If an object speeds up, the net work done on it is positive. (credit: modification of work by “Jassen”/ Flickr)Īccording to this theorem, when an object slows down, its final kinetic energy is less than its initial kinetic energy, the change in its kinetic energy is negative, and so is the net work done on it. ![]() The work done by the horses pulling on the load results in a change in kinetic energy of the load, ultimately going faster. For the mathematical functions describing the motion of a physical particle, we can rearrange the differentials dt, etc., as algebraic quantities in this expression, that is,įigure 7.11 Horse pulls are common events at state fairs. Newton’s second law tells us that F → net = m ( d v → / d t ), F → net = m ( d v → / d t ), so d W net = m ( d v → / d t ) Let’s start by looking at the net work done on a particle as it moves over an infinitesimal displacement, which is the dot product of the net force and the displacement: d W net = F → net Therefore, we should consider the work done by all the forces acting on a particle, or the net work, to see what effect it has on the particle’s motion. We have discussed how to find the work done on a particle by the forces that act on it, but how is that work manifested in the motion of the particle? According to Newton’s second law of motion, the sum of all the forces acting on a particle, or the net force, determines the rate of change in the momentum of the particle, or its motion. Use the work-energy theorem to find information about the forces acting on a particle, given information about its motion. ![]()
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