Concept explainers
(a)
Maximum speed of the needle.
(a)
Answer to Problem 83P
Maximum speed is
Explanation of Solution
Consider the needle is fired horizontally from a spring. Maximum speed occurs just after the needle leaves the spring, before entering the body.
Write the law of conservation of energy for this case.
Here
Write the equation for initial and final kinetic energy.
Here
Write down the equation for initial and elastic potential energy.
Here
Write the equation for work done by the spring
Here
As the initial velocity s zero,
As there is no penetration into the body, distance covered is zero. Then
As there is no extension,
Substitute these results in (I) and write for
Conclusion:
Substitute
Maximum speed is
(b)
Speed to limit the penetration to
(b)
Answer to Problem 83P
Speed should be
Explanation of Solution
The initial elastic potential energy is converted partially into internal energy in the organ and partially kinetic energy of the needle.
Write the energy conservation equation for this case.
Here
Write the equation for initial and final work done by the spring
Here,
As the initial velocity s zero
As there is no extension,
Substitute (II), (III), (VII), (VIII) and (IX) in (VI) and write for
Conclusion:
Substitute
Speed should be
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Chapter 7 Solutions
Principles of Physics: A Calculus-Based Text
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