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
O120 N120 NQ = ?140 mm40 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 140 mm from the pin O. The jaws grip a bolt 40 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 140 mmb = 40 mm
Q = N
2.Easy
OAB400 NQ = ?150 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 400 NOA = 150 mmOB = 75 mm
Q = N
3.Medium
2 kN2.4 m0.8 m3.2 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 4 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, 0.6 m (horizontally) from A. Find the tension T in the tie.

P = 2 kNAB = 2.4 mheight of C = 4 mheight of DE = 0.8 mhorizontal distance A to K = 0.6 m
T = kN
4.Medium
10 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 10 kN acts on member AB at K, 1.35 m (horizontally) from A. Find the force FBC in member BC.

P = 10 kNL = 6 mH = 2.5 mhorizontal distance A to B = 2.7 mhorizontal distance A to K = 1.35 m
FBC = kN
5.Hard
10 kN3 m1 m1.5 m0.375 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1 m above the ground. A vertical load of 10 kN acts on leg AC at K, 0.375 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 3 mheight of C = 2.5 mheight of DE = 1 mhorizontal distance A to K = 0.375 m
C = kN
6.Hard
F = ?1500 N20 mmABC

A toggle press has two equal links AB and BC, each 120 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 = 120 mmh = 20 mm
F = N

Answer key

  1. 1. Q = 420 N
  2. 2. Q = 800 N
  3. 3. T = 0.1875 kN
  4. 4. FBC = 3.726 kN
  5. 5. C = 1.768 kN
  6. 6. F = 507.1 N

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