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
O120 N120 NQ = ?90 mm20 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 90 mm from the pin O. The jaws grip a bolt 20 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 90 mmb = 20 mm
Q = N
2.Easy
OAB100 NQ = ?240 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 100 N acts at A, 240 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 100 NOA = 240 mmOB = 75 mm
Q = N
3.Medium
OAB200 NQ240 mm75 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 200 N at A (240 mm from O) is balanced by a horizontal force at B (75 mm above O). Find the magnitude of the pin reaction FO.

F = 200 NOA = 240 mmOB = 75 mm
FO = N
4.Medium
10 kN5 m1.8 m2.7 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 the horizontal tie DE is 1.8 m above the ground. A load of 10 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 10 kNAB = 5 mheight of C = 4.5 mheight of DE = 1.8 m
C = kN
5.Hard
F = ?1500 N25 mmABC

A toggle press has two equal links AB and BC, each 120 mm long between pins. The joint B sits 25 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1500 N at the slider C? Neglect friction and weights.

Q = 1500 NAB = BC = 120 mmh = 25 mm
F = N
6.Hard
w = 3 kN/m6 kN1.2 m0.8 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 3 kN/m over its full length and a point load of 6 kN at its free end B. Find the force FCD in the strut.

w = 3 kN/mP = 6 kNAD = 1.2 mAB = 2 mAC = 1 m
FCD = kN

Answer key

  1. 1. Q = 540 N
  2. 2. Q = 320 N
  3. 3. FO = 670.5 N
  4. 4. C = 6.814 kN
  5. 5. F = 639 N
  6. 6. FCD = 23.43 kN

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