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 = ?80 mm24 mm

A hand squeezes the handles of a pair of pliers with 60 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 = 60 Na = 80 mmb = 24 mm
Q = N
2.Easy
O200 N200 NQ = ?110 mm24 mm

A hand squeezes the handles of a pair of pliers with 200 N each, 110 mm from the pin O. The jaws grip a bolt 24 mm from the pin. Find the gripping force Q on the bolt.

F = 200 Na = 110 mmb = 24 mm
Q = N
3.Medium
20 kN4 m3 m1.8 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m above the ground and 1.8 m to the right of A. A vertical load of 20 kN acts on member AB at K, 0.45 m (horizontally) from A. Find the force FBC in member BC.

P = 20 kNL = 4 mH = 3 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.45 m
FBC = kN
4.Medium
15 kN6 m1.8 m1.8 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, 3.6 m high, and the horizontal tie DE is 1.8 m above the ground. A load of 15 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 6 mheight of C = 3.6 mheight of DE = 1.8 m
C = kN
5.Hard
2 kN2 kN5 m2 mABC

A uniform horizontal boom AB of weight 2 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 2 kN hangs at B. Find the magnitude of the pin reaction A.

W = 2 kNWb = 2 kNAB = 5 mAC = 2 m
A = kN
6.Hard
F = ?5000 N12 mmABC

A toggle press has two equal links AB and BC, each 200 mm long between pins. The joint B sits 12 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 5000 N at the slider C? Neglect friction and weights.

Q = 5000 NAB = BC = 200 mmh = 12 mm
F = N

Answer key

  1. 1. Q = 200 N
  2. 2. Q = 916.7 N
  3. 3. FBC = 2.79 kN
  4. 4. C = 14.58 kN
  5. 5. A = 7.566 kN
  6. 6. F = 601.1 N

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