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# An experimental apparatus with mass m is placed on a ISBN: 9780321675460 31

## Solution for problem 71P Chapter 7

University Physics | 13th Edition

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Problem 71P

An experimental apparatus with mass ?m? is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance ?x. The apparatus is then released and reaches its maximum height at a distance l?1 above the point where it is released. The apparatus is not attached to the spring, and at its maximum height it is no longer in contact with the spring. The maximum magnitude or acceleration the apparatus can have without being damaged is a, where ?a? > ?g?. (a) What should the force constant of the spring be? (b) What distance ?x? must the spring be compressed initially?

Step-by-Step Solution:

Solution to 71P Step 1 Mass of the experimental apparatus=m Spring constant of the spring=k Acceleration of experimental apparatus when it is released=a Distance the spring was compressed =x Maximum height achieved once spring is released =h Step 2 When the spring is released, the apparatus will reach a height of h and will have a gravitational potential energy U. This potential energy is equal to the potential energy of spring when it is compressed to x. kx /2=mgh………………………………………………………………………………(1) Writing the force equation, kx-mg=ma kx=ma+mg kx=m(a+g) x=m(a+g)/k………………………………………………………………………………(2) (a)

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##### ISBN: 9780321675460

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