When the spring is compressed, a positive force is required to extend it, and when it is extended, a negative force is required to shorten it, or restore it to its natural length. ![]() It has a unit of Newton per meter (N/m) and a dimension given by MT-2. Therefore, the spring constant is defined as the force required to displace the spring by one meter. Since by the definition of work done,W F.s Fs cos(angle between f and s),thus whenever angle is >90, cos(angle) is negative and hence work done is negative. Since by the definition of work done,W F.s Fs cos (angle between f and s),thus whenever angle is >90, cos (angle) is negative and hence work done is negative. The minus sign in F = -kx is there by convention we think of F as the restoring force. The magnitude of the spring constant is given by, k F/x. Whenever a given force and displacement produced by that force has an angle >90 degrees,the work done is said to be negative. We define the coordinate x so that it is negative when the spring is compressed, zero at the natural length and positive when the spring is extended. Work - constant force and distance diagram - spring force and distance. potential energy of the spring and the gravitational potential energy of the object and. When a body is moved as a result of a force being applied to it - work is done. It is possible because of its stored elastic potential energy. Whenever a spring is compressed or stretched, it returns to its standard shape when the stress is relieved. It is because the spring stores potential energy. ![]() At that point, the upward force produced by the spring is exactly balancing the gravitational force on the mass and spring (remember that the spring itself has mass). more work done (a) if they are stretched using the same force. Springs regain their regular shape despite putting force on them by compressing or stretching them. For each mass hung on it (the mass could be zero), a spring has some natural length, at which it is neither compressed (shortened) or extended (lengthened). The diagram defines all of the important dimensions and terms for a coil spring. Where k is called the force constant or spring constant of the spring. Hooke's law says that the force produced by a spring is proportional to the displacement (linear amount of stretching or compressing) of that spring: $$F = -kx$$ The amount of work done by a constant force can be expressed as.
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