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
O100 N100 NQ80 mm15 mm

The handles of a pair of pliers are squeezed with 100 N each, 80 mm from the pin O, and the jaws grip a wire 15 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 100 Na = 80 mmb = 15 mm
FO = N
2.Easy
O120 N120 NQ = ?140 mm15 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 140 mm from the pin O. The jaws grip a bolt 15 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 140 mmb = 15 mm
Q = N
3.Medium
6 kN4 m1.5 m1.5 m1.5 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4 m apart, with its apex pin C 3 m high and the horizontal tie DE 1.5 m above the ground. A vertical load of 6 kN acts on leg AC at K, 1.5 m (horizontally) from A. Find the tension T in the tie.

P = 6 kNAB = 4 mheight of C = 3 mheight of DE = 1.5 mhorizontal distance A to K = 1.5 m
T = kN
4.Medium
OAB150 NQ150 mm80 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (150 mm from O) is balanced by a horizontal force at B (80 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 150 mmOB = 80 mm
FO = N
5.Hard
w = 5 kN/m3 kN1 m0.5 m1 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1 m below A). The beam carries a uniform load of 5 kN/m over its full length and a point load of 3 kN at its free end B. Find the force FCD in the strut.

w = 5 kN/mP = 3 kNAD = 1 mAB = 1.5 mAC = 1 m
FCD = kN
6.Hard
6 kN5 m0.8 m1.6 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, 2.4 m high, and are tied by the horizontal bar DE at 0.8 m. A horizontal force of 6 kN to the right acts at C. Find the tension T in the tie.

P = 6 kNAB = 5 mheight of C = 2.4 mheight of DE = 0.8 m
T = kN

Answer key

  1. 1. FO = 633.3 N
  2. 2. Q = 1120 N
  3. 3. T = 3 kN
  4. 4. FO = 318.8 N
  5. 5. FCD = 14.32 kN
  6. 6. T = 4.5 kN

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