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 = ?180 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 400 N acts at A, 180 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 400 NOA = 180 mmOB = 120 mm
Q = N
2.Easy
OAB80 NQ = ?150 mm50 mm

The bell crank shown turns about the pin O. A vertical force of 80 N acts at A, 150 mm from O, and is balanced by a horizontal force Q at B, 50 mm above O. Find Q.

F = 80 NOA = 150 mmOB = 50 mm
Q = N
3.Medium
OAB300 NQ150 mm100 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 300 N at A (150 mm from O) is balanced by a horizontal force at B (100 mm above O). Find the magnitude of the pin reaction FO.

F = 300 NOA = 150 mmOB = 100 mm
FO = N
4.Medium
500 NQ = ?25°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 25° with the line AC. A downward force of 500 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 500 Nθ = 25°
Q = N
5.Hard
10 kN1 kN2 m2 mABC

A uniform horizontal boom AB of weight 1 kN is pinned to a wall at A and held by a cable from its end B to the point C on the wall, 2 m above A. A load of 10 kN hangs at B. Find the tension T in the cable.

W = 10 kNWb = 1 kNAB = 2 mAC = 2 m
T = kN
6.Hard
15 kN8 kN8 m4 m2.4 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 4 m high and 2.4 m to the right of A. Member AB carries a vertical load of 15 kN at K, 0.6 m (horizontally) from A, and a horizontal load of 8 kN to the right acts at B on member AB. Find the size of the horizontal reaction Ax at A.

P = 15 kNQ = 8 kNL = 8 mH = 4 mhorizontal distance A to B = 2.4 mhorizontal distance A to K = 0.6 m
Ax = kN

Answer key

  1. 1. Q = 600 N
  2. 2. Q = 240 N
  3. 3. FO = 540.8 N
  4. 4. Q = 536.1 N
  5. 5. T = 14.85 kN
  6. 6. Ax = 0.825 kN

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