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
O100 N100 NQ = ?100 mm40 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 100 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 100 mmb = 40 mm
Q = N
2.Easy
O100 N100 NQ110 mm15 mm

The handles of a pair of pliers are squeezed with 100 N each, 110 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 FO that the pin transmits.

F = 100 Na = 110 mmb = 15 mm
FO = N
3.Medium
15 kN3 m4 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 4 m above the ground and 1.8 m to the right of A. A vertical load of 15 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 15 kNL = 3 mH = 4 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.9 m
FBC = kN
4.Medium
6 kN4 m4 m0.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 4 m above the ground and 0.6 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.24 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 4 mH = 4 mhorizontal distance A to B = 0.6 mhorizontal distance A to K = 0.24 m
FBC = kN
5.Hard
w = 4 kN/m10 kN0.8 m1.6 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 = 0.8 mAB = 2.4 mAC = 0.6 m
FCD = kN
6.Hard
5 kN1 kN5 m2.5 mABC

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, 2.5 m above A. A load of 5 kN hangs at B. Find the magnitude of the pin reaction A.

W = 5 kNWb = 1 kNAB = 5 mAC = 2.5 m
A = kN

Answer key

  1. 1. Q = 250 N
  2. 2. FO = 833.3 N
  3. 3. FBC = 4.698 kN
  4. 4. FBC = 0.4725 kN
  5. 5. FCD = 74 kN
  6. 6. A = 11.01 kN

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