(3) Work. For a variable force, work is defined as the integral of force over the...

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(3) Work. For a variable force, work is defined as the integral of force over the given distance: -L W = F(x) dx. Written again to visualize common units units (in meters): W Joules = 1 FC a F(x) dx Newtons meters According to Hooke's law, the force required to compress or stretch a spring from its equilibrium to position x is given by F(x)=kx; With units: F(x) = Newtons Newtons/meters meters for the spring constant k. The value of k is unique to each spring, and it is always positive. (a) A spring can be stretched 0.2 meters from its equilibrium position with force of 40 N. Determine the spring constant. (b) The same spring from part (a) has a natural (total) length of 7 meters. The spring is then stretched to the total length of 10 meters. Determine how much work was required to stretch the spring from its natural length of 7 m to a total length of 10 m. (3) Work. For a variable force, work is defined as the integral of force over the given distance: -L W = F(x) dx. Written again to visualize common units units (in meters): W Joules = 1 FC a F(x) dx Newtons meters According to Hooke's law, the force required to compress or stretch a spring from its equilibrium to position x is given by F(x)=kx; With units: F(x) = Newtons Newtons/meters meters for the spring constant k. The value of k is unique to each spring, and it is always positive. (a) A spring can be stretched 0.2 meters from its equilibrium position with force of 40 N. Determine the spring constant. (b) The same spring from part (a) has a natural (total) length of 7 meters. The spring is then stretched to the total length of 10 meters. Determine how much work was required to stretch the spring from its natural length of 7 m to a total length of 10 m.