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
OAB250 NQ = ?120 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 250 NOA = 120 mmOB = 150 mm
Q = N
2.Easy
O200 N200 NQ = ?120 mm20 mm

A hand squeezes the handles of a pair of pliers with 200 N each, 120 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 200 Na = 120 mmb = 20 mm
Q = N
3.Medium
8 kN4 m1.2 m0.8 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, 2 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 4 mheight of C = 2 mheight of DE = 1.2 m
C = kN
4.Medium
12 kN8 m2 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 2 m above the ground and 4.8 m to the right of A. A vertical load of 12 kN acts on member AB at K, 2.4 m (horizontally) from A. Find the force FBC in member BC.

P = 12 kNL = 8 mH = 2 mhorizontal distance A to B = 4.8 mhorizontal distance A to K = 2.4 m
FBC = kN
5.Hard
5 kN4.8 m1.5 m3 m1.2 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 4.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 5 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 4.8 mheight of C = 4.5 mheight of DE = 1.5 mhorizontal distance A to K = 1.2 m
C = kN
6.Hard
8 kN2 m1.5 m2.1 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 3.6 m high, and are tied by the horizontal bar DE at 1.5 m. A horizontal force of 8 kN to the right acts at C. Find the tension T in the tie.

P = 8 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.5 m
T = kN

Answer key

  1. 1. Q = 200 N
  2. 2. Q = 1200 N
  3. 3. C = 10.77 kN
  4. 4. FBC = 6.792 kN
  5. 5. C = 1.601 kN
  6. 6. T = 6.857 kN

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