Frames & machines worksheet with answers

The handles of a pair of pliers are squeezed with 100 N each, 140 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force F_O that the pin transmits.

The handles of a pair of pliers are squeezed with 40 N each, 140 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.

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 5° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

The bell crank shown turns about the pin O. A vertical force of 200 N at A (200 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction F_O.

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 8 kN acts on leg AC at K, 2.25 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 4.5 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.