Answer:
a) [tex]k = 26666.667\,\frac{N}{m}[/tex], b) [tex]F = 800\,N[/tex], c) [tex]U_{k} = 21.333\,J[/tex], [tex]F = -1066.667\,N[/tex]
Explanation:
a) An expression that relates the work done on spring, its force constant and elongation is given by the definition of elastic potential energy:
[tex]U_{k} = \frac{1}{2}\cdot k \cdot x^{2}[/tex]
The force constant is:
[tex]k = \frac{2\cdot U_{k}}{x^{2}}[/tex]
[tex]k = \frac{2\cdot (12\,J)}{(0.03\,m)^{2}}[/tex]
[tex]k = 26666.667\,\frac{N}{m}[/tex]
b) The magnitude force needed is:
[tex]F = k\cdot x[/tex]
[tex]F = (26666.667\,\frac{N}{m} )\cdot (0.03\,m)[/tex]
[tex]F = 800\,N[/tex]
c) The work needed is:
[tex]U_{k} = \frac{1}{2}\cdot (26666.667\,\frac{N}{m} )\cdot (-0.04\,m)^{2}[/tex]
[tex]U_{k} = 21.333\,J[/tex]
Likewise, the force needed to compress the spring is:
[tex]F = (26666.667\,\frac{N}{m} )\cdot (-0.04\,m)[/tex]
[tex]F = -1066.667\,N[/tex]
