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
O120 N120 NQ120 mm20 mm

The handles of a pair of pliers are squeezed with 120 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 = 120 Na = 120 mmb = 20 mm
FO = N
2.Easy
O100 N100 NQ110 mm15 mm

The handles of a pair of pliers are squeezed with 100 N each, 110 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 100 Na = 110 mmb = 15 mm
FO = N
3.Medium
12 kN1.5 m1 m1 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 m below A. A load of 12 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 12 kNAD = 1.5 mAB = 2.5 mAC = 1 m
A = kN
4.Medium
15 kN1 m1.5 m1 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 m below A. A load of 15 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 15 kNAD = 1 mAB = 2.5 mAC = 1 m
A = kN
5.Hard
4 kN2.4 m0.8 m1.7 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart. The legs meet at the pin C, 2.5 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 2.4 mheight of C = 2.5 mheight of DE = 0.8 m
T = kN
6.Hard
10 kN1 kN2 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 = 2 mAC = 1.5 m
T = kN

Answer key

  1. 1. FO = 840 N
  2. 2. FO = 833.3 N
  3. 3. A = 31.05 kN
  4. 4. A = 43.73 kN
  5. 5. T = 2.941 kN
  6. 6. T = 17.5 kN

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