Answer:
a) [tex]F_{person} = 360.87\,N[/tex], b) [tex]W_{person} = 332\,J[/tex], c) [tex]F_{person} = 721.739\,N[/tex]
Explanation:
a) The system can be described by the Principle of Energy Conservation and Work-Energy Theorem:
[tex]U_{A} + W_{person} = U_{B}[/tex]
The work done to compress the springs is:
[tex]W_{person} = 83\,J[/tex]
The force needed to compress the springs is:
[tex]F_{person} = \frac{83\,J}{0.23\,m}[/tex]
[tex]F_{person} = 360.87\,N[/tex]
b) Spring potential energy is directly proportional to the squared of elongation. Then:
[tex]U_{B} - U_{A} = 83\,J\cdot \frac{(0.46\,m)^{2}}{(0.23\,m)^{2}}[/tex]
[tex]U_{B} - U_{A} = 332\,J[/tex]
[tex]W_{person} = 332\,J[/tex]
c) The force needed to compress the springs is:
[tex]F_{person} = \frac{332\,J}{0.46\,m}[/tex]
[tex]F_{person} = 721.739\,N[/tex]
