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Lesson Worksheet: Triangle of Forces Mathematics
In this worksheet, we will practice solving problems about the equilibrium of a particle under the action of three forces meeting at a point using the resultant of forces or triangle of force method.
Complete the following: If three coplanar and equilibrium forces are represented by the sides of a triangle taken in one cyclic order, then the lengths of the sides of the triangle are proportional to .
- Athe squares of the magnitudes of the forces
- Bthe magnitude of the forces
- Cthe square of the angles
- Dthe angles
Anthony is attempting a mechanics problem in which three coplanar forces , , and are acting on a body. He needs to determine whether the body is in equilibrium or not. He remembers his teacher saying something about checking whether he could arrange the forces into a triangle. So, he draws the shown figure.
Anthony concludes that the three forces are in equilibrium. Is he correct?
Which of the following best describes what he has done?
- AHe has put the forces in the wrong order. He should have started with the force represented by the longest arrow and worked his way to the shortest.
- BHe has not paid attention to the direction of the forces. All the forces should meet head-to-tail. However, in his diagram, and meet head-to-head. Therefore, the forces do not actually form a triangle.
- CHe has used the wrong method; a force triangle is not a valid way of checking for equilibrium.
- DHe has done nothing wrong.
A uniform rod of length 50 cm and weight 143 N is freely suspended at its ends from the ceiling by means of two perpendicular strings attached to the same point on the ceiling. Given that the length of one of the strings is 30 cm, determine the tension in each string.
- A85.8 N, 114.4 N
- B238.33 N, 114.4 N
- C85.8 N, 178.75 N
- D238.33 N, 178.75 N