(Solved):   b) It is postulated that the force acting on a body moving in a circular path is proportio ...

 

b) It is postulated that the force acting on a body moving in a circular path is proportional to its mass, \( m \), velocity, \( v \), and radius, \( r \), as follows: \[ F \propto m v r \] Use dimensional analysis to confirm the relationship and develop a final formula for the force, F. c) An analogue-to-digital converter (ADC), manufactured by your signals division, records hundreds of voltage samples of a linear waveform, measured in \( \mathrm{mV} \), for quality assurance purposes. The samples commence as \( 5,8,11,14,17 \)........etc. Your test colleague has asked you to assist by determining a formula that describes the sequence in terms of the \( n^{\text {th }} \) term of that sequence, and then to use that formula to determine the value of the \( 372^{\text {nd }} \) sample, which has failed to be recorded correctly. The final stage of the process requires the summation of all samples up to and including the \( 372^{\text {nd }} \) sample. Determine a formula to produce the result of this summation. A digital chip, made by your Microelectronics division, counts continuously in the sequence: \( 32,64,128,256, \ldots \) You have been asked to determine a formula to calculate the \( n^{\text {th }} \) count of the chip. Now apply your formula to work out the value of the \( 15^{\text {th }} \) count.