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
OAB200 NQ = ?300 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 200 NOA = 300 mmOB = 80 mm
Q = N
2.Easy
O80 N80 NQ90 mm35 mm

The handles of a pair of pliers are squeezed with 80 N each, 90 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 = 80 Na = 90 mmb = 35 mm
FO = N
3.Medium
OAB250 NQ100 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 N at A (100 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 100 mmOB = 75 mm
FO = N
4.Medium
10 kN4 m2 m1.8 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 m above the ground and 1.8 m to the right of A. A vertical load of 10 kN acts on member AB at K, 0.72 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 4 mH = 2 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.72 m
FBC = kN
5.Hard
4 kN5 kN5 m4 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 4 m high and 2.25 m to the right of A. Member AB carries a vertical load of 4 kN at K, 1.688 m (horizontally) from A, and a horizontal load of 5 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 4 kNQ = 5 kNL = 5 mH = 4 mhorizontal distance A to B = 2.25 mhorizontal distance A to K = 1.688 m
Ax = kN
6.Hard
15 kN1 kN2 m2.5 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, 2.5 m above A. A load of 15 kN hangs at B. Find the magnitude of the pin reaction A.

W = 15 kNWb = 1 kNAB = 2 mAC = 2.5 m
A = kN

Answer key

  1. 1. Q = 750 N
  2. 2. FO = 285.7 N
  3. 3. FO = 416.7 N
  4. 4. FBC = 2.676 kN
  5. 5. Ax = 1.322 kN
  6. 6. A = 12.41 kN

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