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
O200 N200 NQ120 mm15 mm

The handles of a pair of pliers are squeezed with 200 N each, 120 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 = 200 Na = 120 mmb = 15 mm
FO = N
2.Easy
O80 N80 NQ140 mm20 mm

The handles of a pair of pliers are squeezed with 80 N each, 140 mm from the pin O, and the jaws grip a wire 20 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 140 mmb = 20 mm
FO = N
3.Medium
250 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° with the line AC. A downward force of 250 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 250 Nθ = 25°
Q = N
4.Medium
10 kN3 m1 m2 m1.125 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3 m apart, with its apex pin C 3 m high and the horizontal tie DE 1 m above the ground. A vertical load of 10 kN acts on leg AC at K, 1.125 m (horizontally) from A. Find the tension T in the tie.

P = 10 kNAB = 3 mheight of C = 3 mheight of DE = 1 mhorizontal distance A to K = 1.125 m
T = kN
5.Hard
4 kN1.5 kN6 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 its end B to the point C on the wall, 1 m above A. A load of 4 kN hangs at B. Find the tension T in the cable.

W = 4 kNWb = 1.5 kNAB = 6 mAC = 1 m
T = kN
6.Hard
w = 4 kN/m15 kN1 m1.4 m0.75 mABCD

The beam AB of the wall bracket shown is pinned at A and propped by the strut CD (C is 0.75 m below A). The beam carries a uniform load of 4 kN/m over its full length and a point load of 15 kN at its free end B. Find the force FCD in the strut.

w = 4 kN/mP = 15 kNAD = 1 mAB = 2.4 mAC = 0.75 m
FCD = kN

Answer key

  1. 1. FO = 1800 N
  2. 2. FO = 640 N
  3. 3. Q = 268.1 N
  4. 4. T = 2.813 kN
  5. 5. T = 28.89 kN
  6. 6. FCD = 79.2 kN

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