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
O200 N200 NQ120 mm18 mm

The handles of a pair of pliers are squeezed with 200 N each, 120 mm from the pin O, and the jaws grip a wire 18 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 200 Na = 120 mmb = 18 mm
FO = N
2.Easy
12 kN1.2 m0.3 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 1.2 mAB = 1.5 mAC = 0.6 m
FCD = kN
3.Medium
OAB120 NQ200 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 120 N at A (200 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 120 NOA = 200 mmOB = 120 mm
FO = N
4.Medium
5 kN0.8 m1.7 m0.6 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.6 m below A. A load of 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 0.8 mAB = 2.5 mAC = 0.6 m
A = kN
5.Hard
8 kN2.4 m1 m1.4 m0.72 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 2.4 m high and the horizontal tie DE 1 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.72 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2.4 mheight of C = 2.4 mheight of DE = 1 mhorizontal distance A to K = 0.72 m
C = kN
6.Hard
4 kN2 m1.8 m2.7 m0.6 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.8 m above the ground. A vertical load of 4 kN acts on leg AC at K, 0.6 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 4 kNAB = 2 mheight of C = 4.5 mheight of DE = 1.8 mhorizontal distance A to K = 0.6 m
C = kN

Answer key

  1. 1. FO = 1533 N
  2. 2. FCD = 33.54 kN
  3. 3. FO = 233.2 N
  4. 4. A = 23.39 kN
  5. 5. C = 3.161 kN
  6. 6. C = 1.28 kN

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