Work-Variable Force

Work-Variable Force - 0. The force exerted by the spring...

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Work: variable force In the previous discussion we have assumed that the force acting on the object is constant (not dependent on position and/or time). However, in many cases this is not a correct assumption. By reducing the size of the displacement (for example by reducing the time interval) we can obtain an interval over which the force is almost constant. The work done over this small interval (dW) can be calculated The total work done by the force F is the sum of all dW Example: The Spring An example of a varying force is the force exerted by a spring that is stretched or compressed. Suppose we define our coordinate system such that its origin coincides with the end point of a spring in its relaxed state (see Figure 7.7). The spring is stretched if x > 0 and compressed if x <
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Unformatted text preview: 0. The force exerted by the spring will attempt to return the spring to its relaxed state: if x &lt; 0: F &gt; 0 if x &gt; 0: F &lt; 0 It is found experimentally that for many springs the force is proportional to x: F = - k x Figure 7.7. Relaxed, Stretched and Compressed Springs. where k is the spring constant (which is positive and independent of x). The SI units for the spring constant is N/m. The larger the spring constant, the stiffer the spring. The work done by the spring on an object attached to its end can be calculated if we know the initial position x i and final position x f of the object: If the spring is initially in its relaxed state (x i = 0) we find that the work done by the spring is Figure 7.8. Pendulum in x-y plane...
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Work-Variable Force - 0. The force exerted by the spring...

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