Lesson Worksheet: Equilibrium of a Rigid Body Mathematics

In this worksheet, we will practice solving problems about the equilibrium of rigid bodies in 2D where the sum of forces and the sum of moments equal zero.

Q1:

In the given figure, determine the magnitude of the force 𝐹 that makes the rod in equilibrium, given that the magnitude of the given force is 7 N and cosπœƒ=45.

  • A856 N
  • B14√35 N
  • C85√36 N
  • D1709 N

Q2:

A ladder 𝐴𝐡 weighing 34 kg-wt and having a length of 14 m is resting in a vertical plane with its end 𝐡 on a smooth floor and its end 𝐴 against a smooth vertical wall. The end 𝐡, which is 3.3 m away from the wall, is attached by a string to a point on the floor directly below 𝐴. Given that the weight of the ladder is acting on the ladder itself at a point 5.6 m away from 𝐡, find the tension in the string when a man of weight 74 kg-wt stands on the mid-point of the ladder.

Q3:

A ladder 𝐴𝐡 weighing 40√3 kg-wt and having a length of 5 m is resting in a vertical plane with end 𝐡 on a smooth floor and end 𝐴 against a smooth vertical wall. End 𝐡 is attached by a string to a point on the floor vertically below 𝐴. Given that 𝐡 is 2.5 m away from the wall, and the weight of the ladder is acting at a point on the ladder 2 m away from 𝐡, find the tension in the string.

  • A20√3 kg-wt
  • B48 kg-wt
  • C16√3 kg-wt
  • D16 kg-wt

Q4:

A uniform ladder 𝐴𝐡 having a length 𝐿 and weighing 40 kg-wt is resting with one of its ends on a smooth floor and the other against a smooth vertical wall. The ladder makes an angle of 45∘ with the horizontal, and its lower end 𝐴 is attached to a string that is fixed to a point at the junction of the wall and floor. Given that the maximum tension the string can withstand is 60 kg-wt, find how far up the ladder a man of weight 140 kg-wt can go before the string breaks.

  • A27𝐿
  • B14𝐿
  • C17𝐿
  • D12𝐿

Q5:

𝐴𝐡 is a uniform rod of length 140 cm and weight 45 kg-wt. Its end 𝐴 is fixed to a vertical wall by a hinge. It is held horizontally in equilibrium by means of a string of length 70 cm connected to point 𝐢 on the rod, which is 56 cm away from 𝐴, and fixed to a point 𝐷 on the vertical wall vertically above 𝐴. Calculate the tension in the string.

Q6:

A uniform rod that has a length of 128 cm and a weight of 10 N is attached from one of its ends to a hinge that is fixed on a vertical wall. A weight of 10 N is suspended from the rod at a point located 96 cm away from the hinge. The rod is kept in a horizontal position by a string which is attached to the opposite end of the rod from the hinge and fixed to a point on the wall directly above the hinge. Given that the string is inclined to the horizontal at an angle of 60∘, determine the tension 𝑇 in the string, the reaction of the hinge 𝑅, and the angle πœƒ between the reaction’s line of action and the horizontal ground rounded to the nearest minute.

  • A𝑇=5√393N, 𝑅=25√33N, πœƒ=466β€²βˆ˜
  • B𝑇=5√393N, 𝑅=25√33N, πœƒ=4354β€²βˆ˜
  • C𝑇=5√393N, 𝑅=5√393N, πœƒ=466β€²βˆ˜
  • D𝑇=25√33N, 𝑅=5√393N, πœƒ=466β€²βˆ˜
  • E𝑇=25√33N, 𝑅=5√393N, πœƒ=4354β€²βˆ˜

Q7:

A uniform rod 𝐴𝐡 weighing 111 N is resting in a vertical plane with its upper end 𝐴 against a smooth vertical wall and its lower end 𝐡 on a rough horizontal floor. If the rod is resting in limiting equilibrium when inclined by an angle of 30∘ to the horizontal, find the coefficient of friction πœ‡ between the rod and the floor and the reaction of the wall π‘…οŒΊ at its upper end 𝐴 rounded to two decimal places.

  • Aπœ‡=0.29, 𝑅=32.04N
  • Bπœ‡=0.29, 𝑅=384.52N
  • Cπœ‡=0.58, 𝑅=64.09N
  • Dπœ‡=0.87, 𝑅=128.17N
  • Eπœ‡=0.87, 𝑅=96.13N

Q8:

A uniform beam 𝐴𝐡 of weight 106 N is resting with its end 𝐴 on a rough horizontal ground and with its end 𝐡 against a rough vertical wall, where the coefficient of friction between the beam and the wall is 4 times that between the beam and the ground. If the beam is about to move when it is inclined to the wall at an angle whose tangent is 1445, determine the reaction of the wall rounded to two decimal places.

Q9:

A uniform ladder of weight 72 N is resting with its upper end against a smooth vertical wall and its lower end against a rough horizontal ground, where the coefficient of friction between the ladder and the ground is √35. When a force of magnitude 12 N acts on the lower end of the ladder trying to move it away from the wall in a direction upward of the horizontal, where the force makes an angle of 30∘ with the horizontal, the ladder is about to slide. Determine the tangent of the angle that the ladder makes with the horizontal ground.

  • A√35
  • B10√33
  • C5√33
  • D5√34

Q10:

A uniform rod 𝐴𝐡 of weight 10 N and length 12.5 m is resting with its end 𝐴 on a rough horizontal plane and point 𝐢 (between 𝐴 and 𝐡) resting against a smooth horizontal nail, which is 5.7 m above the horizontal plane. If the rod is about to slide when it is inclined to the horizontal at an angle whose tangent is 34, determine the coefficient of friction between the rod and the horizontal plane.

  • A611
  • B1019
  • C1011
  • D56

This lesson includes 75 additional questions and 670 additional question variations for subscribers.

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