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
OAB200 NQ = ?180 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 200 NOA = 180 mmOB = 80 mm
Q = N
2.Easy
O120 N120 NQ = ?150 mm18 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 150 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 150 mmb = 18 mm
Q = N
3.Medium
15 kN4 m2 m1.2 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 2 m above the ground and 1.2 m to the right of A. A vertical load of 15 kN acts on member AB at K, 0.48 m (horizontally) from A. Find the force FBC in member BC.

P = 15 kNL = 4 mH = 2 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.48 m
FBC = kN
4.Medium
12 kN4 m0.8 m1.6 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 2.4 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 12 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the tension T in the tie.

P = 12 kNAB = 4 mheight of C = 2.4 mheight of DE = 0.8 mhorizontal distance A to K = 1.5 m
T = kN
5.Hard
8 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 its end B to the point C on the wall, 2.5 m above A. A load of 8 kN hangs at B. Find the tension T in the cable.

W = 8 kNWb = 1 kNAB = 5 mAC = 2.5 m
T = kN
6.Hard
12 kN1.5 kN3 m4 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, 4 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 1.5 kNAB = 3 mAC = 4 m
T = kN

Answer key

  1. 1. Q = 450 N
  2. 2. Q = 1000 N
  3. 3. FBC = 3.097 kN
  4. 4. T = 5.625 kN
  5. 5. T = 19.01 kN
  6. 6. T = 15.94 kN

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