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
O40 N40 NQ = ?140 mm40 mm

A hand squeezes the handles of a pair of pliers with 40 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 = 40 Na = 140 mmb = 40 mm
Q = N
2.Easy
5 kN2 m1.6 m1.2 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.2 m below A. A load of 5 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 5 kNAD = 2 mAB = 3.6 mAC = 1.2 m
FCD = kN
3.Medium
6 kN5 m2.5 m1.5 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 5 m apart, and B is 2.5 m above the ground and 1.5 m to the right of A. A vertical load of 6 kN acts on member AB at K, 0.9 m (horizontally) from A. Find the force FBC in member BC.

P = 6 kNL = 5 mH = 2.5 mhorizontal distance A to B = 1.5 mhorizontal distance A to K = 0.9 m
FBC = kN
4.Medium
500 NQ = ?12°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 12° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 500 Nθ = 12°
Q = N
5.Hard
20 kN3.2 m1.5 m1 m0.64 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 20 kN acts on leg AC at K, 0.64 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 3.2 mheight of C = 2.5 mheight of DE = 1.5 mhorizontal distance A to K = 0.64 m
C = kN
6.Hard
6 kN5 m1 m1.4 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 5 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 6 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 6 kNAB = 5 mheight of C = 2.4 mheight of DE = 1 mhorizontal distance A to K = 1.5 m
C = kN

Answer key

  1. 1. Q = 140 N
  2. 2. FCD = 17.49 kN
  3. 3. FBC = 1.858 kN
  4. 4. Q = 1176 N
  5. 5. C = 7.547 kN
  6. 6. C = 3.684 kN

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