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
O80 N80 NQ = ?140 mm25 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 140 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 140 mmb = 25 mm
Q = N
2.Easy
O40 N40 NQ120 mm24 mm

The handles of a pair of pliers are squeezed with 40 N each, 120 mm from the pin O, and the jaws grip a wire 24 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 40 Na = 120 mmb = 24 mm
FO = N
3.Medium
15 kN2.4 m0.8 m3.2 m0.9 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 4 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.9 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 2.4 mheight of C = 4 mheight of DE = 0.8 mhorizontal distance A to K = 0.9 m
T = kN
4.Medium
12 kN4.8 m1 m2 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 3 m high and the horizontal tie DE 1 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 4.8 mheight of C = 3 mheight of DE = 1 mhorizontal distance A to K = 1.8 m
T = kN
5.Hard
8 kN3 kN2 m2 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2 m above A. A load of 8 kN hangs at B. Find the tension T in the cable.

W = 8 kNWb = 3 kNAB = 2 mAC = 2 m
T = kN
6.Hard
w = 4 kN/m10 kN0.6 m1.4 m0.6 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.6 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 10 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 10 kNAD = 0.6 mAB = 2 mAC = 0.6 m
FCD = kN

Answer key

  1. 1. Q = 448 N
  2. 2. FO = 240 N
  3. 3. T = 2.109 kN
  4. 4. T = 5.4 kN
  5. 5. T = 13.44 kN
  6. 6. FCD = 66 kN

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