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
OAB400 NQ = ?120 mm75 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 120 mm from O, and is balanced by a horizontal force Q at B, 75 mm above O. Find Q.

F = 400 NOA = 120 mmOB = 75 mm
Q = N
2.Easy
12 kN1.5 m0.9 m1 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1 m below A. A load of 12 kN hangs at the free end B. Neglect the weights. Find the force FCD in the strut.

P = 12 kNAD = 1.5 mAB = 2.4 mAC = 1 m
FCD = kN
3.Medium
8 kN6 m2 m2 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 6 m apart, with its apex pin C 4 m high and the horizontal tie DE 2 m above the ground. A vertical load of 8 kN acts on leg AC at K, 0.75 m (horizontally) from A. Find the tension T in the tie.

P = 8 kNAB = 6 mheight of C = 4 mheight of DE = 2 mhorizontal distance A to K = 0.75 m
T = kN
4.Medium
12 kN2 m1.2 m1.3 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, 2.5 m high, and the horizontal tie DE is 1.2 m above the ground. A load of 12 kN acts at C. Find the magnitude of the force C that the pin C exerts on leg BC.

P = 12 kNAB = 2 mheight of C = 2.5 mheight of DE = 1.2 m
C = kN
5.Hard
F = ?1000 N15 mmABC

A toggle press has two equal links AB and BC, each 80 mm long between pins. The joint B sits 15 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 1000 N at the slider C? Neglect friction and weights.

Q = 1000 NAB = BC = 80 mmh = 15 mm
F = N
6.Hard
6 kN2 m1.2 m1.2 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, 2.4 m high, and are tied by the horizontal bar DE at 1.2 m. A horizontal force of 6 kN to the right acts at C. Find the tension T in the tie.

P = 6 kNAB = 2 mheight of C = 2.4 mheight of DE = 1.2 m
T = kN

Answer key

  1. 1. Q = 640 N
  2. 2. FCD = 34.61 kN
  3. 3. T = 1.5 kN
  4. 4. C = 7.57 kN
  5. 5. F = 381.8 N
  6. 6. T = 6 kN

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