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
O50 N50 NQ = ?120 mm24 mm

A hand squeezes the handles of a pair of pliers with 50 N each, 120 mm from the pin O. The jaws grip a bolt 24 mm from the pin. Find the gripping force Q on the bolt.

F = 50 Na = 120 mmb = 24 mm
Q = N
2.Easy
O120 N120 NQ80 mm25 mm

The handles of a pair of pliers are squeezed with 120 N each, 80 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 = 120 Na = 80 mmb = 25 mm
FO = N
3.Medium
12 kN0.5 m1 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 B. Neglect the weights. Find the magnitude of the pin force A on the beam at A.

P = 12 kNAD = 0.5 mAB = 1.5 mAC = 1 m
A = kN
4.Medium
5 kN3.2 m0.8 m1.7 m0.8 mABCDEK

The A-frame shown stands on a pin at A and a roller at B, 3.2 m apart, with its apex pin C 2.5 m high and the horizontal tie DE 0.8 m above the ground. A vertical load of 5 kN acts on leg AC at K, 0.8 m (horizontally) from A. Find the tension T in the tie.

P = 5 kNAB = 3.2 mheight of C = 2.5 mheight of DE = 0.8 mhorizontal distance A to K = 0.8 m
T = kN
5.Hard
10 kN10 kN4 m4 m1.2 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 4 m high and 1.2 m to the right of A. Member AB carries a vertical load of 10 kN at K, 0.72 m (horizontally) from A, and a horizontal load of 10 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 10 kNQ = 10 kNL = 4 mH = 4 mhorizontal distance A to B = 1.2 mhorizontal distance A to K = 0.72 m
Ax = kN
6.Hard
4 kN3.2 m1.8 m2.7 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, 4.5 m high, and are tied by the horizontal bar DE at 1.8 m. A horizontal force of 4 kN to the right acts at C. Find the tension T in the tie.

P = 4 kNAB = 3.2 mheight of C = 4.5 mheight of DE = 1.8 m
T = kN

Answer key

  1. 1. Q = 250 N
  2. 2. FO = 504 N
  3. 3. A = 30 kN
  4. 4. T = 1.176 kN
  5. 5. Ax = 1.74 kN
  6. 6. T = 3.333 kN

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