Theory question 117
Statics(a) A particle is under the action of forces P = (4N, 030°) and R = (10N, 300°). Find the force that will keep the particle in equilibrium.
(b) A train travelling at 45 ms−1 is brought to rest after covering a distance of 1500m. Find the: (i) time taken to come to rest; (ii) uniform retardation.
Show the model answer
Model answer
(a) East/north components: P = (2, 3.464), R = (−8.660, 5).
Resultant = (−6.660, 8.464). The equilibrant is (6.660, −8.464).
Magnitude = √(44.36 + 71.64) = 10.77 N; bearing = 180° − tan⁻¹(6.660/8.464) = 141.8°.
Force = (10.77 N, 141.8°).
(b)(i) s = ½(u + v)t: 1500 = 22.5t, t = 66.7 s.
(ii) 0 = 45² + 2a(1500), a = −0.675; retardation 0.675 ms⁻².
Explanation
The equilibrant is equal and opposite to the resultant.