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
O40 N40 NQ80 mm25 mm

The handles of a pair of pliers are squeezed with 40 N each, 80 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 = 40 Na = 80 mmb = 25 mm
FO = N
2.Easy
15 kN2 m1.2 m3.3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 4.5 m high, and are tied together by the horizontal bar DE at a height of 1.2 m. A load of 15 kN acts at C. Find the tension T in the tie DE.

P = 15 kNAB = 2 mheight of C = 4.5 mheight of DE = 1.2 m
T = kN
3.Medium
10 kN2 m1.5 m2.5 m0.25 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 4 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 10 kN acts on leg AC at K, 0.25 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 2 mheight of C = 4 mheight of DE = 1.5 mhorizontal distance A to K = 0.25 m
T = kN
4.Medium
15 kN3.2 m1 m3 m0.64 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 4 m high and the horizontal tie DE 1 m above the ground. A vertical load of 15 kN acts on leg AC at K, 0.64 m (horizontally) from A. Find the tension T in the tie.

P = 15 kNAB = 3.2 mheight of C = 4 mheight of DE = 1 mhorizontal distance A to K = 0.64 m
T = kN
5.Hard
F = ?2500 N25 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2500 N at the slider C? Neglect friction and weights.

Q = 2500 NAB = BC = 120 mmh = 25 mm
F = N
6.Hard
15 kN0.5 kN3 m2 mABC

A uniform horizontal boom AB of weight 0.5 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 15 kN hangs at B. Find the magnitude of the pin reaction A.

W = 15 kNWb = 0.5 kNAB = 3 mAC = 2 m
A = kN

Answer key

  1. 1. FO = 168 N
  2. 2. T = 2.273 kN
  3. 3. T = 0.5 kN
  4. 4. T = 1.6 kN
  5. 5. F = 1065 N
  6. 6. A = 22.88 kN

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