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
O50 N50 NQ90 mm25 mm

The handles of a pair of pliers are squeezed with 50 N each, 90 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 = 50 Na = 90 mmb = 25 mm
FO = N
2.Easy
O80 N80 NQ150 mm30 mm

The handles of a pair of pliers are squeezed with 80 N each, 150 mm from the pin O, and the jaws grip a wire 30 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 150 mmb = 30 mm
FO = N
3.Medium
6 kN3 m3 m1.35 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 above the ground and 1.35 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.3375 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 3 mH = 3 mhorizontal distance A to B = 1.35 mhorizontal distance A to K = 0.3375 m
FBC = kN
4.Medium
400 NQ = ?15°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 15° with the line AC. A downward force of 400 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 400 Nθ = 15°
Q = N
5.Hard
10 kN1 kN4 m1.5 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 1.5 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 1 kNAB = 4 mAC = 1.5 m
T = kN
6.Hard
F = ?2000 N5 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 5 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 = 200 mmh = 5 mm
F = N

Answer key

  1. 1. FO = 230 N
  2. 2. FO = 480 N
  3. 3. FBC = 0.7704 kN
  4. 4. Q = 746.4 N
  5. 5. T = 29.9 kN
  6. 6. F = 100 N

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