Theory question 107
DynamicsA body of mass 5kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4 − j. Calculate the;
(a) velocity of the body;
(b) magnitude of its velocity, after 4 seconds.
Show the model answer
Model answer
Resultant force = (6 + 5 + 4)i + (2 + 4 − 1)j = 15i + 5j N
a = F/m = (15i + 5j)/5 = 3i + j ms⁻²
(a) Starting from rest, v = at = 4(3i + j) = 12i + 4j ms⁻¹
(b) |v| = √(12² + 4²) = √160 = 4√10 ≈ 12.65 ms⁻¹
Explanation
Add the forces, use F = ma, then v = u + at with u = 0.