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 NQ150 mm30 mm

The handles of a pair of pliers are squeezed with 60 N each, 150 mm from the pin O, and the jaws grip a wire 30 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 60 Na = 150 mmb = 30 mm
FO = N
2.Easy
OAB50 NQ = ?180 mm80 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 80 mm above O. Find Q.

F = 50 NOA = 180 mmOB = 80 mm
Q = N
3.Medium
OAB80 NQ120 mm150 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 80 N at A (120 mm from O) is balanced by a horizontal force at B (150 mm above O). Find the magnitude of the pin reaction FO.

F = 80 NOA = 120 mmOB = 150 mm
FO = N
4.Medium
150 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 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 = 8°
Q = N
5.Hard
5 kN4.8 m2 m1.6 m1.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 4.8 m apart, with its apex pin C 3.6 m high and the horizontal tie DE 2 m above the ground. A vertical load of 5 kN acts on leg AC at K, 1.8 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 5 kNAB = 4.8 mheight of C = 3.6 mheight of DE = 2 mhorizontal distance A to K = 1.8 m
C = kN
6.Hard
8 kN2.4 m1 m1 m0.3 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2.4 m apart, with its apex pin C 2 m high and the horizontal tie DE 1 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.3 m (horizontally) from A. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 8 kNAB = 2.4 mheight of C = 2 mheight of DE = 1 mhorizontal distance A to K = 0.3 m
C = kN

Answer key

  1. 1. FO = 360 N
  2. 2. Q = 112.5 N
  3. 3. FO = 102.4 N
  4. 4. Q = 533.7 N
  5. 5. C = 3.38 kN
  6. 6. C = 1.562 kN

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