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 NQ120 mm24 mm

The handles of a pair of pliers are squeezed with 200 N each, 120 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 = 200 Na = 120 mmb = 24 mm
FO = N
2.Easy
OAB150 NQ = ?200 mm150 mm

The bell crank shown turns about the pin O. A vertical force of 150 N acts at A, 200 mm from O, and is balanced by a horizontal force Q at B, 150 mm above O. Find Q.

F = 150 NOA = 200 mmOB = 150 mm
Q = N
3.Medium
5 kN1.5 m1.5 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 5 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 5 kNAD = 1.5 mAB = 3 mAC = 0.75 m
A = kN
4.Medium
4 kN1 m0.5 m0.75 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 0.75 m below A. A load of 4 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 4 kNAD = 1 mAB = 1.5 mAC = 0.75 m
A = kN
5.Hard
6 kN6 kN4 m3 m2.4 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 4 m apart, and B is 3 m high and 2.4 m to the right of A. Member AB carries a vertical load of 6 kN at K, 0.6 m (horizontally) from A, and a horizontal load of 6 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 6 kNQ = 6 kNL = 4 mH = 3 mhorizontal distance A to B = 2.4 mhorizontal distance A to K = 0.6 m
Ax = kN
6.Hard
F = ?2500 N10 mmABC

A toggle press has two equal links AB and BC, each 150 mm long between pins. The joint B sits 10 mm above the line AC. Which downward force F at B produces a horizontal pressing force of 2500 N at the slider C? Neglect friction and weights.

Q = 2500 NAB = BC = 150 mmh = 10 mm
F = N

Answer key

  1. 1. FO = 1200 N
  2. 2. Q = 200 N
  3. 3. A = 20.62 kN
  4. 4. A = 8.246 kN
  5. 5. Ax = 3.12 kN
  6. 6. F = 334.1 N

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