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
O40 N40 NQ = ?80 mm18 mm

A hand squeezes the handles of a pair of pliers with 40 N each, 80 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 40 Na = 80 mmb = 18 mm
Q = N
2.Easy
6 kN1 m1.5 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 6 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 1 mAB = 2.5 mAC = 0.5 m
FCD = kN
3.Medium
OAB200 NQ150 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (150 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 150 mmOB = 80 mm
FO = N
4.Medium
4 kN2.4 m1.2 m2.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 2.4 mheight of C = 4 mheight of DE = 1.2 m
C = kN
5.Hard
6 kN1.5 kN2.5 m3 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 3 m above A. A load of 6 kN hangs at B. Find the tension T in the cable.

W = 6 kNWb = 1.5 kNAB = 2.5 mAC = 3 m
T = kN
6.Hard
2 kN0.5 kN3 m1.5 mABC

A uniform horizontal boom AB of weight 0.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 1.5 m above A. A load of 2 kN hangs at B. Find the tension T in the cable.

W = 2 kNWb = 0.5 kNAB = 3 mAC = 1.5 m
T = kN

Answer key

  1. 1. Q = 177.8 N
  2. 2. FCD = 33.54 kN
  3. 3. FO = 425 N
  4. 4. C = 2.176 kN
  5. 5. T = 8.787 kN
  6. 6. T = 5.031 kN

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