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 NQ120 mm20 mm

The handles of a pair of pliers are squeezed with 150 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 = 150 Na = 120 mmb = 20 mm
FO = N
2.Easy
6 kN1.6 m0.4 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 6 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 6 kNAD = 1.6 mAB = 2 mAC = 1.2 m
FCD = kN
3.Medium
4 kN0.8 m0.7 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 4 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 4 kNAD = 0.8 mAB = 1.5 mAC = 0.75 m
A = kN
4.Medium
10 kN1 m1.4 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 10 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 10 kNAD = 1 mAB = 2.4 mAC = 0.8 m
A = kN
5.Hard
8 kN3.2 m1.5 m1 m1.2 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 2.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 8 kN acts on leg AC at K, 1.2 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 3.2 mheight of C = 2.5 mheight of DE = 1.5 mhorizontal distance A to K = 1.2 m
C = kN
6.Hard
6 kN1.5 kN6 m4 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 4 m above A. A load of 6 kN hangs at B. Find the tension T in the cable.

W = 6 kNWb = 1.5 kNAB = 6 mAC = 4 m
T = kN

Answer key

  1. 1. FO = 1050 N
  2. 2. FCD = 12.5 kN
  3. 3. A = 8.732 kN
  4. 4. A = 33.11 kN
  5. 5. C = 5.66 kN
  6. 6. T = 12.17 kN

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