Calculus Questions

Q1.

A spring has a natural length of 5 cm. A work of 5 Joule stretched a spring from 7 cm to a length off) cm. a) (2 marks) Find the spring constant, k b) (3 marks} If 10 joule of work is applied to the same spring from its natural length, to what length the spring is stretched to? Use Calculus to solve this question, no mark will be given if you use energy equation A bucket of grain needs to be lifted up to height of 20 m. The bucket weigh 2 kg. Initially, there is 15 kg of grain in the bucket. However, there is a small hole in it and by the time the bucket reached 10 m height, there is only 12 kg grain left in the bucket. If it is assumed that the grains leaks at a constant rate, how much work is required to raise the bucket and the grain to the top. Ignore the weight if rope/cable