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 NQ90 mm18 mm

The handles of a pair of pliers are squeezed with 40 N each, 90 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 = 40 Na = 90 mmb = 18 mm
FO = N
2.Easy
O50 N50 NQ = ?150 mm25 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 150 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 150 mmb = 25 mm
Q = N
3.Medium
5 kN6 m0.6 m1.4 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 6 m apart. The legs meet at the pin C, 2 m high, and the horizontal tie DE is 0.6 m above the ground. A load of 5 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 6 mheight of C = 2 mheight of DE = 0.6 m
C = kN
4.Medium
150 NQ = ?30°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 30° with the line AC. A downward force of 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 30°
Q = N
5.Hard
20 kN4 m1.2 m0.8 m0.8 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 m high and the horizontal tie DE 1.2 m above the ground. A vertical load of 20 kN acts on leg AC at K, 0.8 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 4 mheight of C = 2 mheight of DE = 1.2 mhorizontal distance A to K = 0.8 m
C = kN
6.Hard
6 kN8 kN6 m4 m1.8 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 high and 1.8 m to the right of A. Member AB carries a vertical load of 6 kN at K, 0.45 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 6 kNQ = 8 kNL = 6 mH = 4 mhorizontal distance A to B = 1.8 mhorizontal distance A to K = 0.45 m
Ax = kN

Answer key

  1. 1. FO = 240 N
  2. 2. Q = 300 N
  3. 3. C = 5.912 kN
  4. 4. Q = 129.9 N
  5. 5. C = 10.77 kN
  6. 6. Ax = 1.927 kN

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