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
O80 N80 NQ100 mm24 mm

The handles of a pair of pliers are squeezed with 80 N each, 100 mm from the pin O, and the jaws grip a wire 24 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 80 Na = 100 mmb = 24 mm
FO = N
2.Easy
5 kN1.2 m1.2 m0.8 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.8 m below A. A load of 5 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 5 kNAD = 1.2 mAB = 2.4 mAC = 0.8 m
FCD = kN
3.Medium
250 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 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 = 8°
Q = N
4.Medium
6 kN0.6 m0.9 m0.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.5 m below A. A load of 6 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 6 kNAD = 0.6 mAB = 1.5 mAC = 0.5 m
A = kN
5.Hard
F = ?3000 N30 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 30 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 3000 N at the slider C? Neglect friction and weights.

Q = 3000 NAB = BC = 150 mmh = 30 mm
F = N
6.Hard
10 kN5 m1 m1.4 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, 2.4 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 5 mheight of C = 2.4 mheight of DE = 1 m
T = kN

Answer key

  1. 1. FO = 413.3 N
  2. 2. FCD = 18.03 kN
  3. 3. Q = 889.4 N
  4. 4. A = 20.12 kN
  5. 5. F = 1225 N
  6. 6. T = 8.571 kN

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