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
O100 N100 NQ = ?80 mm15 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 80 mm from the pin O. The jaws grip a bolt 15 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 80 mmb = 15 mm
Q = N
2.Easy
O150 N150 NQ = ?110 mm18 mm

A hand squeezes the handles of a pair of pliers with 150 N each, 110 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 150 Na = 110 mmb = 18 mm
Q = N
3.Medium
OAB120 NQ200 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (200 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 120 NOA = 200 mmOB = 120 mm
FO = N
4.Medium
20 kN6 m2 m2.5 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 2 m above the ground. A vertical load of 20 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the tension T in the tie.

P = 20 kNAB = 6 mheight of C = 4.5 mheight of DE = 2 mhorizontal distance A to K = 1.8 m
T = kN
5.Hard
w = 4 kN/m8 kN1.6 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 4 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 = 4 kN/mP = 8 kNAD = 1.6 mAB = 3 mAC = 1.5 m
FCD = kN
6.Hard
8 kN0.5 kN6 m4 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, 4 m above A. A load of 8 kN hangs at B. Find the magnitude of the pin reaction A.

W = 8 kNWb = 0.5 kNAB = 6 mAC = 4 m
A = kN

Answer key

  1. 1. Q = 533.3 N
  2. 2. Q = 916.7 N
  3. 3. FO = 233.2 N
  4. 4. T = 7.2 kN
  5. 5. FCD = 38.38 kN
  6. 6. A = 12.38 kN

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