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
OAB50 NQ = ?250 mm100 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 100 mm above O. Find Q.

F = 50 NOA = 250 mmOB = 100 mm
Q = N
2.Easy
8 kN5 m1 m1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 2 m high, and are tied together by the horizontal bar DE at a height of 1 m. A load of 8 kN acts at C. Find the tension T in the tie DE.

P = 8 kNAB = 5 mheight of C = 2 mheight of DE = 1 m
T = kN
3.Medium
15 kN6 m4 m0.9 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 4 m above the ground and 0.9 m to the right of A. A vertical load of 15 kN acts on member AB at K, 0.225 m (horizontally) from A. Find the force FBC in member BC.

P = 15 kNL = 6 mH = 4 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.225 m
FBC = kN
4.Medium
20 kN2.4 m1.5 m2.1 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, 3.6 m high, and the horizontal tie DE is 1.5 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1.5 m
C = kN
5.Hard
10 kN2.4 m0.6 m1.4 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, 2 m high, and are tied by the horizontal bar DE at 0.6 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 2.4 mheight of C = 2 mheight of DE = 0.6 m
T = kN
6.Hard
15 kN1.5 kN3 m1.5 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, 1.5 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 1.5 kNAB = 3 mAC = 1.5 m
T = kN

Answer key

  1. 1. Q = 125 N
  2. 2. T = 10 kN
  3. 3. FBC = 0.9115 kN
  4. 4. C = 11.52 kN
  5. 5. T = 7.143 kN
  6. 6. T = 35.22 kN

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