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 = ?200 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 50 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 = 50 NOA = 200 mmOB = 150 mm
Q = N
2.Easy
O200 N200 NQ150 mm35 mm

The handles of a pair of pliers are squeezed with 200 N each, 150 mm from the pin O, and the jaws grip a wire 35 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 200 Na = 150 mmb = 35 mm
FO = N
3.Medium
5 kN3 m0.6 m1.9 m0.9 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.6 m above the ground. A vertical load of 5 kN acts on leg AC at K, 0.9 m (horizontally) from A. Find the tension T in the tie.

P = 5 kNAB = 3 mheight of C = 2.5 mheight of DE = 0.6 mhorizontal distance A to K = 0.9 m
T = kN
4.Medium
10 kN6 m3 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 3 m above the ground and 0.9 m to the right of A. A vertical load of 10 kN acts on member AB at K, 0.225 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 6 mH = 3 mhorizontal distance A to B = 0.9 mhorizontal distance A to K = 0.225 m
FBC = kN
5.Hard
4 kN2 m1.2 m2.4 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 2 mheight of C = 3.6 mheight of DE = 1.2 mhorizontal distance A to K = 0.6 m
C = kN
6.Hard
5 kN6 kN5 m2 m2.25 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 2 m high and 2.25 m to the right of A. Member AB carries a vertical load of 5 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 5 kNQ = 6 kNL = 5 mH = 2 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. Q = 66.67 N
  2. 2. FO = 1057 N
  3. 3. T = 1.184 kN
  4. 4. FBC = 0.7396 kN
  5. 5. C = 1.3 kN
  6. 6. Ax = 1.463 kN

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