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
O50 N50 NQ = ?150 mm35 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 35 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 150 mmb = 35 mm
Q = N
2.Easy
O100 N100 NQ = ?100 mm35 mm

A hand squeezes the handles of a pair of pliers with 100 N each, 100 mm from the pin O. The jaws grip a bolt 35 mm from the pin. Find the gripping force Q on the bolt.

F = 100 Na = 100 mmb = 35 mm
Q = N
3.Medium
3 kN0.8 m1.2 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 3 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 3 kNAD = 0.8 mAB = 2 mAC = 1.2 m
A = kN
4.Medium
6 kN1.2 m2.8 m1 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 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 = 1.2 mAB = 4 mAC = 1 m
A = kN
5.Hard
8 kN5 m1.2 m3.3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 5 m apart. The legs meet at the pin C, 4.5 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 8 kN to the right acts at C. Find the tension T in the tie.

P = 8 kNAB = 5 mheight of C = 4.5 mheight of DE = 1.2 m
T = kN
6.Hard
20 kN5 m1 m3 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 4 m high and the horizontal tie DE 1 m above the ground. A vertical load of 20 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 = 20 kNAB = 5 mheight of C = 4 mheight of DE = 1 mhorizontal distance A to K = 1.5 m
C = kN

Answer key

  1. 1. Q = 214.3 N
  2. 2. Q = 285.7 N
  3. 3. A = 6.727 kN
  4. 4. A = 27.78 kN
  5. 5. T = 5.455 kN
  6. 6. C = 7.81 kN

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