Put the ideas to work.

A sensor is suspended from a small ring by a light vertical cord. The ring is held by an inclined spring on its left and a light horizontal cord on its right, as shown in Figure 2. The spring slopes upwards to the left at 40.0° above the horizontal. The sensor's weight is 12.0 N. The ring and cords have negligible mass. All forces act in one plane through the centre of the ring, which is at rest. The spring constant is 80.0 N m⁻¹ and the spring obeys Hooke's law for extensions up to 0.300 m. (a) Use vertical equilibrium to calculate the tension in the inclined spring. [3] (b) Calculate the tension in the horizontal cord. [2] (c) Calculate the spring's extension and check whether using Hooke's law is consistent with the stated proportional range. [3] (d) A pupil claims that the spring tension is 12.0 N because the sensor is at rest. Explain why this claim is incorrect. [2]