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(II) The resistance of a packing material to a sharp object penetrating it is a force proportional to the fourth power of the penetration depth $x ;$ that is, $\vec { \mathbf { F } } = - k x ^ { 4 } \hat { \mathbf { i } }$ . Calculate the work done to force a sharp object a distance $d$ into the material.

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$\frac{1}{5} k d^{5}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

Hope College

University of Winnipeg

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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So here we know that X initial equals zero and we're going to see the X Final equals de Soto. Find the work done. We simply have to integrate the force function from zero to d d x. So it'll be the integral from absurdity of f of x o f sub x times d x So this is going to equal zero d of K x to the fourth times D X and this legal K D to the fifth over five. So the work is going to be equal to the spring constant times rather the coefficient in this case, k d to the fifth over five. And then this would be in the of course, the eye direction. So this would be our final answer. That is the end of solution. Thank you for watching.

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