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
OAB250 NQ = ?120 mm100 mm

The bell crank shown turns about the pin O. A vertical force of 250 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 100 mm above O. Find Q.

F = 250 NOA = 120 mmOB = 100 mm
Q = N
2.Easy
O80 N80 NQ = ?120 mm25 mm

A hand squeezes the handles of a pair of pliers with 80 N each, 120 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 80 Na = 120 mmb = 25 mm
Q = N
3.Medium
6 kN0.8 m1.2 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 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 = 0.8 mAB = 2 mAC = 0.75 m
A = kN
4.Medium
8 kN4 m1.2 m1.3 m0.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.5 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 4 mheight of C = 2.5 mheight of DE = 1.2 mhorizontal distance A to K = 0.5 m
T = kN
5.Hard
F = ?4000 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 4000 N at the slider C? Neglect friction and weights.

Q = 4000 NAB = BC = 150 mmh = 30 mm
F = N
6.Hard
4 kN4 m1 m3.5 m1 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1 m above the ground. A vertical load of 4 kN acts on leg AC at K, 1 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 4 mheight of C = 4.5 mheight of DE = 1 mhorizontal distance A to K = 1 m
C = kN

Answer key

  1. 1. Q = 300 N
  2. 2. Q = 384 N
  3. 3. A = 18.36 kN
  4. 4. T = 1.538 kN
  5. 5. F = 1633 N
  6. 6. C = 1.152 kN

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