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26.5: The Work-Energy Theorem

Last updated

Aug 8, 2024
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- 26.4: Conservation of Energy
- 26.6: The Virial Theorem

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Not only can energy be converted from one form to another, but it can also be converted into work, and vice versa. If a force is applied to a moving body over some distance, then work is done on the body, causing a change in its kinetic energy. The change in kinetic energy of the body is equal to the amount of work done. This result is called the work-energy theorem:

$W=\Delta K$

Example $\PageIndex{1}$

Suppose a body of mass $1000 \mathrm{~kg}$ is moving at a speed of $50 \mathrm{~m} / \mathrm{s}$ . then its kinetic energy is $K=m v^{2} / 2=1,250,000 \mathrm{~J}$ . If we now do a work of $200,000 \mathrm{~J}$ on the body in the direction of motion what is its final velocity

Solution

By the work-energy theorem its kinetic energy will increase to $1,450,000 \mathrm{~J}$ . Its final velocity will then be $v=\sqrt{2 K / m}=53.85 \mathrm{~m} / \mathrm{s}$ .

Example 26.5.1\PageIndex{1}

Solution

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Example $\PageIndex{1}$