Final answer:
To compress a spring with a spring constant of 160 N/m an additional 3 cm from an initial compression of 5 cm, 0.312 joules of work is required.
Step-by-step explanation:
The work required to compress a spring can be calculated using the formula for the potential energy stored in a compressed or stretched spring, which is U = 1/2kx², where U is the potential energy in joules, k is the spring constant in newtons per meter (N/m), and x is the displacement of the spring from its equilibrium position in meters.
To find the work required to compress the spring an additional 3 cm when it's already compressed 5 cm, we must calculate the difference in potential energy between the 5 cm compression and the 8 cm (5 cm + 3 cm) compression.
The potential energy at 5 cm compression is U1 = 1/2 × 160 N/m × (0.05 m)² and at 8 cm compression it's U2 = 1/2 × 160 N/m × (0.08 m)².
Calculating both, we get: U1 = 0.2 J and U2 = 0.512 J.
The work done in compressing the spring from 5 cm to 8 cm is the difference between U2 and U1, which is 0.512 J - 0.2 J = 0.312 J.
Therefore, 0.312 joules of work is required to compress the spring an additional 3 cm.