Frames & machines worksheet with answers

Free printable Frames & machines worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
O60 N60 NQ80 mm18 mm

The handles of a pair of pliers are squeezed with 60 N each, 80 mm from the pin O, and the jaws grip a wire 18 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 60 Na = 80 mmb = 18 mm
FO = N
2.Easy
O80 N80 NQ90 mm20 mm

The handles of a pair of pliers are squeezed with 80 N each, 90 mm from the pin O, and the jaws grip a wire 20 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 90 mmb = 20 mm
FO = N
3.Medium
10 kN2.4 m1 m1.5 m0.72 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1 m above the ground. A vertical load of 10 kN acts on leg AC at K, 0.72 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 1 mhorizontal distance A to K = 0.72 m
T = kN
4.Medium
500 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° 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.

F = 500 Nθ = 25°
Q = N
5.Hard
4 kN3 m0.8 m2.8 mABCDE

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, 3.6 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 3 mheight of C = 3.6 mheight of DE = 0.8 m
T = kN
6.Hard
15 kN1.5 kN5 m1.5 mABC

A uniform horizontal boom AB of weight 1.5 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.

W = 15 kNWb = 1.5 kNAB = 5 mAC = 1.5 m
A = kN

Answer key

  1. 1. FO = 326.7 N
  2. 2. FO = 440 N
  3. 3. T = 2.4 kN
  4. 4. Q = 536.1 N
  5. 5. T = 2.571 kN
  6. 6. A = 52.51 kN

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