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
O60 N60 NQ = ?110 mm20 mm

A hand squeezes the handles of a pair of pliers with 60 N each, 110 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 60 Na = 110 mmb = 20 mm
Q = N
2.Easy
O100 N100 NQ90 mm15 mm

The handles of a pair of pliers are squeezed with 100 N each, 90 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 = 90 mmb = 15 mm
FO = N
3.Medium
8 kN2.4 m1.2 m2.4 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, 3.6 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 8 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2.4 mheight of C = 3.6 mheight of DE = 1.2 m
C = kN
4.Medium
OAB100 NQ300 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 100 N at A (300 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 300 mmOB = 80 mm
FO = N
5.Hard
10 kN6 m0.6 m1.9 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 2.5 m high, and are tied by the horizontal bar DE at 0.6 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 6 mheight of C = 2.5 mheight of DE = 0.6 m
T = kN
6.Hard
12 kN1.5 kN3 m2 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, 2 m above A. A load of 12 kN hangs at B. Find the tension T in the cable.

W = 12 kNWb = 1.5 kNAB = 3 mAC = 2 m
T = kN

Answer key

  1. 1. Q = 330 N
  2. 2. FO = 700 N
  3. 3. C = 4.472 kN
  4. 4. FO = 388.1 N
  5. 5. T = 6.579 kN
  6. 6. T = 22.99 kN

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