Frames & machines worksheet with answers

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 240 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

The handles of a pair of pliers are squeezed with 50 N each, 90 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force F_O that the pin transmits.

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 2 m above the ground and 4.8 m to the right of A. A vertical load of 10 kN acts on member AB at K, 1.92 m (horizontally) from A. Find the force F_BC in member BC.

The bell crank shown turns about the pin O. A vertical force of 300 N at A (200 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction F_O.

A toggle press has two equal links AB and BC, each 80 mm long between pins. The joint B sits 12 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 4000 N at the slider C? Neglect friction and weights.

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 1.5 m above A. A load of 15 kN hangs at B. Find the magnitude of the pin reaction A.