S.5 & 6 Moments Couple A Level Mechanics Caltec S.5

Sponsored by The Science Foundation College 0753 80 27 09 Join Now Moments This is a product of th e force multiplied by the perpendicular distance between its line of action and the axis of rotation . The mom ent is also known at turning force or torque Moment (Nm) = Force (N) x perpendicular distance (m) A couple Two forces that are equal in magnitude but opposite in direction (and acting along parallel lines), thus creating the turning effect of a torque or moment . Principle of moments For an object to be in equilibrium (with no movements about a turning point), the sum of anticlockwise moments is equal to the sum of clockwise moments. Examples 1 A rod mass 8kg and 2m long is balance horizontally by two inextensible string tied to the end A and B of the rod when a m ass of 20kg hangs 0.5 m from A . Find the tensions in the strings at A and B. [ take g = 10ms-2] Solution The sum of m oments of initial at A = 0 0 = 0.5 x 200 + 1 x 80 – T2 x 2 T2 = 90 Sponsored by The Science Foundation College 0753 80 27 09 Join Now But T 1 + T 2 = 200 + 80 T1 + 90 = 280 T1 = 190N Example 2 A force of 200N hangs on a uniform rod of weight 80N and held at equilibrium by a string as shown in the figure below . Calculate the tension in the string Solution Taking moments at A T x d = 80 x + 200L But d = L sin 30 TLsin 30 = 240L T = 480N Example 3 A rod of length L weighing 200kg is held by a …