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
10 kN2.4 m2 m2 m0.9 mABCDEK

The A-frame shown rests on a pin at A and a roller at B, 2.4 m apart. A vertical load of 10 kN acts on leg AC at the point K, 0.9 m (horizontally) from A. Find the vertical reaction By at the roller.

P = 10 kNAB = 2.4 mhorizontal distance A to K = 0.9 m
By = kN
2.Easy
O200 N200 NQ = ?90 mm30 mm

A hand squeezes the handles of a pair of pliers with 200 N each, 90 mm from the pin O. The jaws grip a bolt 30 mm from the pin. Find the gripping force Q on the bolt.

F = 200 Na = 90 mmb = 30 mm
Q = N
3.Medium
150 NQ = ?5°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 5° with the line AC. A downward force of 150 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 150 Nθ = 5°
Q = N
4.Medium
100 NQ = ?30°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 30° with the line AC. A downward force of 100 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 100 Nθ = 30°
Q = N
5.Hard
15 kN3 m1.2 m1.8 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 1.2 m above the ground. A vertical load of 15 kN acts on leg AC at K, 1.125 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 15 kNAB = 3 mheight of C = 3 mheight of DE = 1.2 mhorizontal distance A to K = 1.125 m
C = kN
6.Hard
15 kN1 kN4 m2 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2 m above A. A load of 15 kN hangs at B. Find the tension T in the cable.

W = 15 kNWb = 1 kNAB = 4 mAC = 2 m
T = kN

Answer key

  1. 1. By = 3.75 kN
  2. 2. Q = 600 N
  3. 3. Q = 857.3 N
  4. 4. Q = 86.6 N
  5. 5. C = 7.322 kN
  6. 6. T = 34.66 kN

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