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
O150 N150 NQ = ?100 mm18 mm

A hand squeezes the handles of a pair of pliers with 150 N each, 100 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 150 Na = 100 mmb = 18 mm
Q = N
2.Easy
6 kN0.75 m1.25 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 = 0.75 mAB = 2 mAC = 0.5 m
FCD = kN
3.Medium
5 kN2 m0.4 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 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 2 mAB = 2.4 mAC = 0.5 m
A = kN
4.Medium
6 kN4.8 m1.5 m1.5 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 3 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 6 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 4.8 mheight of C = 3 mheight of DE = 1.5 m
C = kN
5.Hard
4 kN4.8 m0.6 m1.4 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 2 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 4 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 4.8 mheight of C = 2 mheight of DE = 0.6 mhorizontal distance A to K = 1.8 m
C = kN
6.Hard
5 kN0.5 kN3 m3 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, 3 m above A. A load of 5 kN hangs at B. Find the tension T in the cable.

W = 5 kNWb = 0.5 kNAB = 3 mAC = 3 m
T = kN

Answer key

  1. 1. Q = 833.3 N
  2. 2. FCD = 28.84 kN
  3. 3. A = 24.02 kN
  4. 4. C = 5.66 kN
  5. 5. C = 2.977 kN
  6. 6. T = 7.425 kN

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