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
O60 N60 NQ = ?140 mm25 mm

A hand squeezes the handles of a pair of pliers with 60 N each, 140 mm from the pin O. The jaws grip a bolt 25 mm from the pin. Find the gripping force Q on the bolt.

F = 60 Na = 140 mmb = 25 mm
Q = N
2.Easy
OAB300 NQ = ?240 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 300 N acts at A, 240 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 300 NOA = 240 mmOB = 80 mm
Q = N
3.Medium
OAB250 NQ240 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 250 N at A (240 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 250 NOA = 240 mmOB = 150 mm
FO = N
4.Medium
12 kN0.75 m1.75 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 12 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 12 kNAD = 0.75 mAB = 2.5 mAC = 1.2 m
A = kN
5.Hard
6 kN6 m0.6 m1.8 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, 2.4 m high, and are tied by the horizontal bar DE at 0.6 m. A horizontal force of 6 kN to the right acts at C. Find the tension T in the tie.

P = 6 kNAB = 6 mheight of C = 2.4 mheight of DE = 0.6 m
T = kN
6.Hard
2 kN1.5 kN2.5 m1 mABC

A uniform horizontal boom AB of weight 1.5 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 1 m above A. A load of 2 kN hangs at B. Find the magnitude of the pin reaction A.

W = 2 kNWb = 1.5 kNAB = 2.5 mAC = 1 m
A = kN

Answer key

  1. 1. Q = 336 N
  2. 2. Q = 900 N
  3. 3. FO = 471.7 N
  4. 4. A = 37.54 kN
  5. 5. T = 4 kN
  6. 6. A = 6.916 kN

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