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
O150 N150 NQ110 mm25 mm

The handles of a pair of pliers are squeezed with 150 N each, 110 mm from the pin O, and the jaws grip a wire 25 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 150 Na = 110 mmb = 25 mm
FO = N
2.Easy
OAB250 NQ = ?250 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 250 NOA = 250 mmOB = 80 mm
Q = N
3.Medium
8 kN3.2 m0.8 m2.2 m0.96 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart, with its apex pin C 3 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.96 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 3.2 mheight of C = 3 mheight of DE = 0.8 mhorizontal distance A to K = 0.96 m
T = kN
4.Medium
OAB200 NQ120 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (120 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 120 mmOB = 120 mm
FO = N
5.Hard
20 kN8 kN8 m3 m3.6 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 high and 3.6 m to the right of A. Member AB carries a vertical load of 20 kN at K, 1.44 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 20 kNQ = 8 kNL = 8 mH = 3 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 1.44 m
Ax = kN
6.Hard
4 kN4 kN3 m3 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 3 m apart, and B is 3 m high and 1.8 m to the right of A. Member AB carries a vertical load of 4 kN at K, 0.9 m (horizontally) from A, and a horizontal load of 4 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 4 kNQ = 4 kNL = 3 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.9 m
Ax = kN

Answer key

  1. 1. FO = 810 N
  2. 2. Q = 781.3 N
  3. 3. T = 1.745 kN
  4. 4. FO = 282.8 N
  5. 5. Ax = 1.68 kN
  6. 6. Ax = 1.92 kN

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