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
2 kN4.8 m1 m1.5 m1.8 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 4.8 m apart. A vertical load of 2 kN acts on leg AC at the point K, 1.8 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 2 kNAB = 4.8 mhorizontal distance A to K = 1.8 m
By = kN
2.Easy
O50 N50 NQ120 mm20 mm

The handles of a pair of pliers are squeezed with 50 N each, 120 mm from the pin O, and the jaws grip a wire 20 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 50 Na = 120 mmb = 20 mm
FO = N
3.Medium
OAB80 NQ120 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (120 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 120 mmOB = 75 mm
FO = N
4.Medium
6 kN8 m3 m1.2 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 above the ground and 1.2 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.48 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 8 mH = 3 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.48 m
FBC = kN
5.Hard
F = ?2000 N15 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 15 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2000 N at the slider C? Neglect friction and weights.

Q = 2000 NAB = BC = 120 mmh = 15 mm
F = N
6.Hard
12 kN2 kN2.5 m2 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 2 kNAB = 2.5 mAC = 2 m
T = kN

Answer key

  1. 1. By = 0.75 kN
  2. 2. FO = 350 N
  3. 3. FO = 150.9 N
  4. 4. FBC = 0.8919 kN
  5. 5. F = 504 N
  6. 6. T = 20.81 kN

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