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 = ?120 mm25 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 120 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 = 120 mmb = 25 mm
Q = N
2.Easy
OAB200 NQ = ?300 mm60 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 60 mm above O. Find Q.

F = 200 NOA = 300 mmOB = 60 mm
Q = N
3.Medium
20 kN4 m0.8 m1.6 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 4 m apart. The legs meet at the pin C, 2.4 m high, and the horizontal tie DE is 0.8 m above the ground. A load of 20 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 20 kNAB = 4 mheight of C = 2.4 mheight of DE = 0.8 m
C = kN
4.Medium
500 NQ = ?8°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 8° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 500 Nθ = 8°
Q = N
5.Hard
6 kN3 kN5 m2 mABC

A uniform horizontal boom AB of weight 3 kN is pinned to a wall at A and held by a cable from B to the point C on the wall, 2 m above A. A load of 6 kN hangs at B. Find the magnitude of the pin reaction A.

W = 6 kNWb = 3 kNAB = 5 mAC = 2 m
A = kN
6.Hard
w = 4 kN/m8 kN1 m1 m1.2 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 1.2 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 8 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 8 kNAD = 1 mAB = 2 mAC = 1.2 m
FCD = kN

Answer key

  1. 1. Q = 240 N
  2. 2. Q = 1000 N
  3. 3. C = 16.01 kN
  4. 4. Q = 1779 N
  5. 5. A = 18.81 kN
  6. 6. FCD = 31.24 kN

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