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 NQ120 mm15 mm

The handles of a pair of pliers are squeezed with 40 N each, 120 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 = 40 Na = 120 mmb = 15 mm
FO = N
2.Easy
5 kN2 m1 m1.5 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, 2.5 m high, and are tied together by the horizontal bar DE at a height of 1 m. A load of 5 kN acts at C. Find the tension T in the tie DE.

P = 5 kNAB = 2 mheight of C = 2.5 mheight of DE = 1 m
T = kN
3.Medium
10 kN3.2 m1.2 m1.8 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart. The legs meet at the pin C, 3 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 3.2 mheight of C = 3 mheight of DE = 1.2 m
C = kN
4.Medium
20 kN4.8 m2 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart. The legs meet at the pin C, 3.6 m high, and the horizontal tie DE is 2 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 4.8 mheight of C = 3.6 mheight of DE = 2 m
C = kN
5.Hard
4 kN1 kN2.5 m1 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 m above A. A load of 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 1 kNAB = 2.5 mAC = 1 m
T = kN
6.Hard
w = 2 kN/m8 kN0.6 m1.4 m1.5 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.5 m below A). The beam carries a uniform load of 2 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 2 kN/mP = 8 kNAD = 0.6 mAB = 2 mAC = 1.5 m
FCD = kN

Answer key

  1. 1. FO = 360 N
  2. 2. T = 1.667 kN
  3. 3. C = 6.69 kN
  4. 4. C = 18.03 kN
  5. 5. T = 12.12 kN
  6. 6. FCD = 35.9 kN

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