Theory question 118
Dynamics(a) Forces F1 = (2N, 210°), F2 = (4N, 120°) act on a particle of mass 7kg which is at rest. Calculate the: (i) acceleration of the particle; (ii) velocity of the particle after 3 seconds
(b) F1 = (2i + 3j)N, F2 = (−5j)N and F3 = (6i − 4j)N act on a body. Find the magnitude and direction of the fourth force that will keep the body in equilibrium.
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(a) Bearings 210° and 120° differ by 90°, so R = √(22 + 42) = √20 = 2√5 ≈ 4.47 N
(components: F1 = (−1, −1.732), F2 = (3.464, −2), sum (2.464, −3.732))
(i) a = R/m = 4.47/7 ≈ 0.64 ms−2
(ii) v = u + at = 0 + 0.639 × 3 ≈ 1.92 ms−1
(b) F1 + F2 + F3 = 8i − 6j, so F4 = −8i + 6j
|F4| = √(64 + 36) = 10 N
Direction: tan−1(6/8) ≈ 36.9° above the negative x-axis, i.e. 143.1° to the positive x-axis (bearing ≈ 306.9°, N53.1°W)
In equilibrium the fourth force is minus the sum of the other three.