Question

Suppose a force of 30 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys​ Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.3 m from its equilibrium​ position? c. How much work is required to stretch the spring 0.2 m from its equilibrium​ position? d. How much additional work is required to stretch the spring 0.1 m if it has already been stretched 0.1 m from its

Answer 1

Explanation:

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Answer 2

a)
`k = 300\,(N)/(m)`, b)
`\Delta U_(k) = 13.5\,J`, c)
`\Delta U_(k) = 6\,J`, d)
`\Delta U_(k) = 4.5\,J`

Explanation:

a) The spring constant is calculated by using this expression:

`k = (F)/(x)`

`k = (30\,N)/(0.1\,m)`

`k = 300\,(N)/(m)`

b) The work needed to compress the spring from its initial position is:

`\Delta U_(k) = (1)/(2)\cdot k \cdot (x_(f)^(2)-x_(o)^(2))`

`\Delta U_(k) = (1)/(2)\cdot (300\,(N)/(m) )\cdot [(-0.3\,m)^(2)-(0\,m)^(2)]`

`\Delta U_(k) = 13.5\,J`

c) The work needed to stretch the spring is:

`\Delta U_(k) = (1)/(2)\cdot (300\,(N)/(m) )\cdot [(0.2\,m)^(2)-(0\,m)^(2)]`

`\Delta U_(k) = 6\,J`

d) The work need to stretch the spring is:

`\Delta U_(k) = (1)/(2)\cdot (300\,(N)/(m) )\cdot [(0.2\,m)^(2)-(0.1\,m)^(2)]`

`\Delta U_(k) = 4.5\,J`