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
OAB100 NQ = ?200 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 200 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 100 NOA = 200 mmOB = 150 mm
Q = N
2.Easy
O150 N150 NQ = ?150 mm24 mm

A hand squeezes the handles of a pair of pliers with 150 N each, 150 mm from the pin O. The jaws grip a bolt 24 mm from the pin. Find the gripping force Q on the bolt.

F = 150 Na = 150 mmb = 24 mm
Q = N
3.Medium
4 kN2.4 m1.5 m2.1 m0.72 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.72 m (horizontally) from A. Find the tension T in the tie.

P = 4 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1.5 mhorizontal distance A to K = 0.72 m
T = kN
4.Medium
15 kN8 m3 m4.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 3 m above the ground and 4.8 m to the right of A. A vertical load of 15 kN acts on member AB at K, 2.4 m (horizontally) from A. Find the force FBC in member BC.

P = 15 kNL = 8 mH = 3 mhorizontal distance A to B = 4.8 mhorizontal distance A to K = 2.4 m
FBC = kN
5.Hard
5 kN1 kN2.5 m2 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 m above A. A load of 5 kN hangs at B. Find the magnitude of the pin reaction A.

W = 5 kNWb = 1 kNAB = 2.5 mAC = 2 m
A = kN
6.Hard
8 kN3 kN4 m2.5 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 2.5 m high and 1.2 m to the right of A. Member AB carries a vertical load of 8 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 3 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 8 kNQ = 3 kNL = 4 mH = 2.5 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. Q = 133.3 N
  2. 2. Q = 937.5 N
  3. 3. T = 0.6857 kN
  4. 4. FBC = 6.58 kN
  5. 5. A = 6.893 kN
  6. 6. Ax = 1.116 kN

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