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
OAB200 NQ = ?300 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 200 N acts at A, 300 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 200 NOA = 300 mmOB = 120 mm
Q = N
2.Easy
O200 N200 NQ90 mm24 mm

The handles of a pair of pliers are squeezed with 200 N each, 90 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 = 90 mmb = 24 mm
FO = N
3.Medium
2 kN1 m2 m1.5 mABCD

A horizontal beam AB is pinned to a wall at A and propped by the strut CD, pinned to the wall at C, 1.5 m below A. A load of 2 kN hangs at B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 2 kNAD = 1 mAB = 3 mAC = 1.5 m
A = kN
4.Medium
8 kN2 m1.8 m2.7 m0.75 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 2 m apart, with its apex pin C 4.5 m high and the horizontal tie DE 1.8 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 = 2 mheight of C = 4.5 mheight of DE = 1.8 mhorizontal distance A to K = 0.75 m
T = kN
5.Hard
10 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 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 2 mheight of C = 2.4 mheight of DE = 1.2 m
T = kN
6.Hard
12 kN2 kN8 m2 m3.6 mABCK

The frame shown has pins at A, B and C; A and C are fixed to the ground 8 m apart, and B is 2 m high and 3.6 m to the right of A. Member AB carries a vertical load of 12 kN at K, 2.7 m (horizontally) from A, and a horizontal load of 2 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 12 kNQ = 2 kNL = 8 mH = 2 mhorizontal distance A to B = 3.6 mhorizontal distance A to K = 2.7 m
Ax = kN

Answer key

  1. 1. Q = 500 N
  2. 2. FO = 950 N
  3. 3. A = 5.657 kN
  4. 4. T = 1.111 kN
  5. 5. T = 10 kN
  6. 6. Ax = 8.01 kN

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