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
OAB50 NQ = ?250 mm120 mm

The bell crank shown turns about the pin O. A vertical force of 50 N acts at A, 250 mm from O, and is balanced by a horizontal force Q at B, 120 mm above O. Find Q.

F = 50 NOA = 250 mmOB = 120 mm
Q = N
2.Easy
O120 N120 NQ = ?140 mm30 mm

A hand squeezes the handles of a pair of pliers with 120 N each, 140 mm from the pin O. The jaws grip a bolt 30 mm from the pin. Find the gripping force Q on the bolt.

F = 120 Na = 140 mmb = 30 mm
Q = N
3.Medium
OAB150 NQ150 mm120 mmFO​ = ?

The bell crank shown turns about the pin O. A vertical force of 150 N at A (150 mm from O) is balanced by a horizontal force at B (120 mm above O). Find the magnitude of the pin reaction FO.

F = 150 NOA = 150 mmOB = 120 mm
FO = N
4.Medium
250 NQ = ?5°ABC

In the toggle clamp shown, two equal links AB and BC are pinned together at B, and each makes 5° with the line AC. A downward force of 250 N is applied at B. The slider C presses on a workpiece. Neglecting friction and weights, find the horizontal clamping force Q.

F = 250 Nθ = 5°
Q = N
5.Hard
15 kN3 m1 m2 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 3 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 15 kN to the right acts at C. Find the tension T in the tie.

P = 15 kNAB = 3 mheight of C = 3 mheight of DE = 1 m
T = kN
6.Hard
10 kN3 m1 m3 mABCDE

The A-frame shown stands on a pin at A and a roller at B, 3 m apart. The legs meet at the pin C, 4 m high, and are tied by the horizontal bar DE at 1 m. A horizontal force of 10 kN to the right acts at C. Find the tension T in the tie.

P = 10 kNAB = 3 mheight of C = 4 mheight of DE = 1 m
T = kN

Answer key

  1. 1. Q = 104.2 N
  2. 2. Q = 560 N
  3. 3. FO = 240.1 N
  4. 4. Q = 1429 N
  5. 5. T = 11.25 kN
  6. 6. T = 6.667 kN

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