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 NQ = ?110 mm20 mm

A hand squeezes the handles of a pair of pliers with 60 N each, 110 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 60 Na = 110 mmb = 20 mm
Q = N
2.Easy
O50 N50 NQ90 mm18 mm

The handles of a pair of pliers are squeezed with 50 N each, 90 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 = 50 Na = 90 mmb = 18 mm
FO = N
3.Medium
2 kN4 m0.8 m3.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 2 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 2 kNAB = 4 mheight of C = 4 mheight of DE = 0.8 m
C = kN
4.Medium
2 kN1.6 m2.4 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 2 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 2 kNAD = 1.6 mAB = 4 mAC = 0.6 m
A = kN
5.Hard
F = ?3000 N20 mmABC

A toggle press has two equal links AB and BC, each 100 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 100 mmh = 20 mm
F = N
6.Hard
10 kN2 kN3 m4 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 4 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 2 kNAB = 3 mAC = 4 m
T = kN

Answer key

  1. 1. Q = 330 N
  2. 2. FO = 300 N
  3. 3. C = 1.179 kN
  4. 4. A = 13.67 kN
  5. 5. F = 1225 N
  6. 6. T = 13.75 kN

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