Final answer:
The work done by a spring force is affected by the spring constant such that an increase in the spring constant results in a greater force for the same displacement, leading to a higher amount of work done. The work is negative for both compression and extension because the spring force is opposite to the displacement. For a spring with a spring constant of 80 N/m, 4 N is needed to compress it 5 cm, and 12 N to expand it 15 cm.
Step-by-step explanation:
The work done by a spring force changes with the spring constant in a specific way. According to Hooke's Law, the force a spring exerts (F) is equal to the negative of the spring constant (k) times the displacement (x), or F = -kx. The negative sign in this equation indicates that the restoring force provided by the spring is in the direction opposite to the displacement.
When considering the work (W) done by a spring force, it is expressed mathematically as the negative integral of the force with respect to displacement, from the initial to the final position. This calculation takes into account the varying force over the displacement. If a spring is compressed or extended from its equilibrium position, work is done by the external force on the spring, and this work is stored as potential energy in the spring.
In the case of compression or extension of a spring, the work is negative because the spring force and the displacement are in opposite directions. When a load is small enough to be moved by the spring force, the spring does positive work while returning to equilibrium, but this doesn't change with the spring constant.
Moreover, an increase in the spring constant (k) results in a higher magnitude of force for a given displacement, thus increasing the work done for that displacement.
To specifically answer part of the original question, let's calculate the force required to compress and expand a spring with a spring constant of 80 N/m. For a compression of 5 cm (or 0.05 m), the force is F = kx = 80 N/m * 0.05 m = 4 N. To expand the spring by 15 cm (or 0.15 m), the force required is F = 80 N/m * 0.15 m = 12 N.