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 NQ150 mm40 mm

The handles of a pair of pliers are squeezed with 200 N each, 150 mm from the pin O, and the jaws grip a wire 40 mm from the pin. Take all forces as perpendicular to the handle. Find the force FO that the pin transmits.

F = 200 Na = 150 mmb = 40 mm
FO = N
2.Easy
O80 N80 NQ140 mm25 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 25 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 = 25 mm
FO = N
3.Medium
6 kN0.8 m1.7 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 6 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 6 kNAD = 0.8 mAB = 2.5 mAC = 0.8 m
A = kN
4.Medium
20 kN2 m1.8 m2.2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 2 m apart. The legs meet at the pin C, 4 m high, and the horizontal tie DE is 1.8 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 = 2 mheight of C = 4 mheight of DE = 1.8 m
C = kN
5.Hard
F = ?3000 N5 mmABC

A toggle press has two equal links AB and BC, each 100 mm long between pins. The joint B sits 5 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 = 100 mmh = 5 mm
F = N
6.Hard
2 kN3.2 m1 m1.4 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3.2 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 2 kN to the right acts at C. Find the tension T in the tie.

P = 2 kNAB = 3.2 mheight of C = 2.4 mheight of DE = 1 m
T = kN

Answer key

  1. 1. FO = 950 N
  2. 2. FO = 528 N
  3. 3. A = 22.67 kN
  4. 4. C = 10.98 kN
  5. 5. F = 300.4 N
  6. 6. T = 1.714 kN

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