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saurabhjain
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Why work done by a force was taken as dot product between force applied and displacement caused?
axmls said:Because 1. We're interested in the component of force that points in the same direction as the motion
The force doesn't have to be the cause of the displacement. The cause is irrelevant for the definition of work.saurabhjain said:Why work done by a force was taken as dot product between force applied and displacement caused?
Yes. In fact, there could be many forces acting on the body, and the body could be moving along a very complicated path because of all the forces. Each force does work, which is calculated using the standard dot product definition of work. In this process, each force could be doing positive, zero or negative work. The algebraic sum of the works done by all the forces, which we can call the net work, can also be calculated by first finding the net force, and then calculating the work by that net force.A.T. said:The force doesn't have to be the cause of the displacement. The cause is irrelevant for the definition of work.
I'm sure you meant the component of force parallel to the displacement. The force could very well be opposite to the displacement, which was Drakkith's point here:axmls said:We're interested in the component of force that points in the same direction as the motion
Drakkith said:What about the work involved in decelerating an object?
Work done by a force is a scalar product because it is the product of two scalar quantities - the magnitude of the force and the displacement in the direction of the force. This results in a scalar value, which represents the amount of energy transferred by the force.
Scalar quantities have only magnitude, while vector quantities have both magnitude and direction. Work done by a force is a scalar quantity because it only considers the magnitude of the force and the displacement, while ignoring the direction of the force.
Work done is directly related to energy, as it is the amount of energy transferred by a force. When a force does work on an object, it transfers energy to the object, causing its energy to increase. In other words, work done is a measure of the change in energy of an object.
The scalar product for work done is calculated by multiplying the magnitude of the force applied to an object with the displacement of the object in the direction of the force. This results in a scalar value, which represents the amount of work done on the object by the force.
The unit of measurement for work done is joules (J), which is the same as the unit for energy. This unit is derived from the base units of mass, length, and time - kilograms, meters, and seconds - and is used to measure the amount of energy transferred by a force to an object.