A nail is placed with its sharp end just touching a piece of wood. When a mass falls with a velocity v and hits the nail, it drives the nail into the wood. It is suggested that the depth d that the nail moves into the wood is related to v by the equation d = kv², where k is a constant.
a. Suggest:
i. The independent, dependent and control variables
ii. How the velocity of the falling mass can be measured as it hits the nail
iii. Sensible values for d and how they may be achieved and measured
iv. The graph to be plotted and what it shows if the relationship is true.
b. Write a logical step-by-step method to test the relationship.