Three forces, (15i + j) N, (5qi – pj) N and (–3pi – qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, find the value of p and the value of q. (Mechanics 1 June 2017)

As the particle is at rest, the net force acting on the particle must be equal to zero, i.e. Fres = 0Therefore, (15i + j) + (5qi - pj) + (-3pi - qj) = 0Collating 'i' terms: 15 + 5q - 3p = 0 (Equation 1)Collating 'j' terms: 1 - p - q = 0 (Equation 2) p = 1-qSubsitute 'p' into Equation 1:15 + 5q - 3(1 - q) = 0Expanding the bracket: 15 + 5q - 3 + 3q = 0Collate terms:12 + 8q = 0 Make 'q' the subject:q = -12/8 = -3/2 (or -1.5)Substituting 'q' to find 'p':p = 1 - (-3/2) = 5/2 (or 2.5)

Answered by Idris K. Maths tutor

11107 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Having a rectangular parking lot with an area of 5,000 square yards that is to be fenced off on the three sides not adjacent to the highway, what is the least amount of fencing that will be needed to complete the job?


How does integration by parts work?


How do I integrate and differentiate 1/(x^2)?


Factorise x^3-6x^2+9x.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences