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
O50 N50 NQ = ?80 mm24 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 80 mm from the pin O. The jaws grip a bolt 24 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 80 mmb = 24 mm
Q = N
2.Easy
12 kN5 m1.8 m2.7 m1.5 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 5 m apart. A vertical load of 12 kN acts on leg AC at the point K, 1.5 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 12 kNAB = 5 mhorizontal distance A to K = 1.5 m
By = kN
3.Medium
6 kN1.6 m1.4 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 6 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 6 kNAD = 1.6 mAB = 3 mAC = 1 m
A = kN
4.Medium
4 kN6 m1.8 m2.2 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, 4 m high, and the horizontal tie DE is 1.8 m above the ground. A load of 4 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 6 mheight of C = 4 mheight of DE = 1.8 m
C = kN
5.Hard
F = ?1500 N20 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 20 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 150 mmh = 20 mm
F = N
6.Hard
15 kN0.5 kN3 m3 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, 3 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 0.5 kNAB = 3 mAC = 3 m
T = kN

Answer key

  1. 1. Q = 166.7 N
  2. 2. By = 3.6 kN
  3. 3. A = 18.75 kN
  4. 4. C = 3.382 kN
  5. 5. F = 403.6 N
  6. 6. T = 21.57 kN

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