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 = ?120 mm18 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 120 mm from the pin O. The jaws grip a bolt 18 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 120 mmb = 18 mm
Q = N
2.Easy
O40 N40 NQ = ?90 mm35 mm

A hand squeezes the handles of a pair of pliers with 40 N each, 90 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 40 Na = 90 mmb = 35 mm
Q = N
3.Medium
15 kN6 m4 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 4 m above the ground and 2.7 m to the right of A. A vertical load of 15 kN acts on member AB at K, 1.62 m (horizontally) from A. Find the force FBC in member BC.

P = 15 kNL = 6 mH = 4 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.62 m
FBC = kN
4.Medium
OAB100 NQ150 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 100 N at A (150 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 100 NOA = 150 mmOB = 150 mm
FO = N
5.Hard
F = ?5000 N30 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 30 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 = 150 mmh = 30 mm
F = N
6.Hard
10 kN5 m1.2 m3.3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 4.5 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 5 mheight of C = 4.5 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. Q = 333.3 N
  2. 2. Q = 102.9 N
  3. 3. FBC = 5.25 kN
  4. 4. FO = 141.4 N
  5. 5. F = 2041 N
  6. 6. T = 6.818 kN

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