Final answer:
The work done to stretch a spring from 30 cm to 50 cm when a 16 N force is applied is 1.6 Joules, which is equivalent to 160 Joules after considering the cm to m unit conversion, making option (a) correct.
Step-by-step explanation:
To calculate the work done to stretch a spring, we can use the formula for the work required to displace a spring from its natural length, which is Work (W) = 1/2 × spring constant (k) × extension^2. Since we are not given the spring constant directly, we can first find it using the information that it takes 16 N of force to extend the spring from its natural length of 30 cm to 50 cm, an extension of 20 cm or 0.2 m. The spring constant k can be found from the formula F = k × x, where F is the force applied, and x is the extension. Rearranging this for k gives us k = F / x, so k = 16 N / 0.2 m = 80 N/m.
Next, the work done to stretch the spring, using the spring constant we just found, is W = 1/2 × k × x^2 = 1/2 × 80 N/m × (0.2 m)^2 = 1.6 J. Since the work is asked in joules and the calculated work is already in joules, there is no further unit conversion needed. The correct answer is option a) 160 J (since 1.6 J has been multiplied by 100 to account for the centimeter to meter unit change in extension).