Question

Three forces, (15i+j) N, 5qi – pj) N and (-3pi - gj) 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.

Answer 1

Given that the particle is in equilibrium, the value of p = 2.5 and the value of q = -1.5

To answer the question, we need to know what force are

What is a force?

A force that thing which cause a change in motion of an object

Since there are 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, the resultant force on the particle is zero.

What is a resultant force?

A resultant force is a vector sum of two or more forces

So,  (15i + j) N + (5qi – pj) N + (-3pi - qj) N = 0i + 0j

15i + 5qi - 3pi + j - pj - qj = 0i + 0j

(15 + 5q - 3p)i + (1 - p - q)j = 0i + 0j

Equating components, we have

15 + 5q - 3p = 0 and 1 - p - q = 0

5q - 3p = -15 (1) and - p - q = -1

5q - 3p = -15 (1) and p + q = 1 (2)

From equation (2), p = 1 - q (3).

The value of q

Substituting p into (1), we have

5q - 3p = -15 (1)

5q - 3(1 - q) = -15

5q - 3 + 3q = -15

5q + 3q = -15 + 3

8q = -12

q = -12/8

q = -3/2

q = - 1.5

The value of p

Substituing q into (3), we have

p = 1 - q

p = 1 - (-3/2)

p = 1 + 3/2

p = (2 + 3)/2

p = 5/2

p = 2.5

So, the value of p = 2.5 and the value of q = -1.5

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