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
O80 N80 NQ = ?110 mm40 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 110 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 110 mmb = 40 mm
Q = N
2.Easy
OAB400 NQ = ?300 mm100 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 100 mm above O. Find Q.

F = 400 NOA = 300 mmOB = 100 mm
Q = N
3.Medium
5 kN6 m2.5 m2.7 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 6 m apart, and B is 2.5 m above the ground and 2.7 m to the right of A. A vertical load of 5 kN acts on member AB at K, 1.35 m (horizontally) from A. Find the force FBC in member BC.

P = 5 kNL = 6 mH = 2.5 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.35 m
FBC = kN
4.Medium
2 kN2 m0.8 m1.7 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 2 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 2 kNAB = 2 mheight of C = 2.5 mheight of DE = 0.8 mhorizontal distance A to K = 0.75 m
T = kN
5.Hard
6 kN0.5 kN2 m1 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, 1 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 0.5 kNAB = 2 mAC = 1 m
A = kN
6.Hard
8 kN0.5 kN2.5 m1 mABC

A uniform horizontal boom AB of weight 0.5 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 1 m above A. A load of 8 kN hangs at B. Find the tension T in the cable.

W = 8 kNWb = 0.5 kNAB = 2.5 mAC = 1 m
T = kN

Answer key

  1. 1. Q = 220 N
  2. 2. Q = 1200 N
  3. 3. FBC = 1.863 kN
  4. 4. T = 0.4412 kN
  5. 5. A = 12.5 kN
  6. 6. T = 22.21 kN

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