# 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 that makes the rod in equilibrium, given that the magnitude of the given force is 7 N and .

- A N
- B N
- C N
- D N

**Q2: **

A ladder weighing 34 kg-wt and having a length of 14 m is resting in a vertical plane with its end on a smooth floor and its end against a smooth vertical wall. The end , which is 3.3 m away from the wall, is attached by a string to a point on the floor directly below . Given that the weight of the ladder is acting on the ladder itself at a point 5.6 m away from , 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 weighing kg-wt and having a length of 5 m is resting in a vertical plane with end on a smooth floor and end against a smooth vertical wall. End is attached by a string to a point on the floor vertically below . Given that 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 , find the tension in the string.

- A kg-wt
- B48 kg-wt
- C kg-wt
- D16 kg-wt

**Q4: **

A uniform ladder having a length 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 with the horizontal, and its lower end is attached to a string that is fixed to a point at the junction of the wall and floor in the same vertical plane which also contains the ladder. 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.

- A
- B
- C
- D

**Q5: **

is a uniform rod of length 140 cm and weight 45 kg-wt. Its end 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 on the rod, which is 56 cm away from , and fixed to a point on the vertical wall vertically above . Calculate the tension in the string.

**Q6: **

A uniform rod that has a length of cm and a weight of N is attached from one of its ends to a hinge that is fixed on a vertical wall. A weight of N is suspended from the rod at a point located 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 , determine the tension in the string, the reaction of the hinge , and the angle between the reactionβs line of action and the horizontal ground rounded to the nearest minute.

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q7: **

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

- A,
- B,
- C,
- D,
- E,

**Q8: **

A uniform beam of weight 106 N is resting with its end on a rough horizontal ground and with its end 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 , determine the reaction of the wall rounded to two decimal places.

**Q9: **

A uniform rod of weight 10 N and length 12.5 m is resting with its end on a rough horizontal plane and point (between and ) 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 , determine the coefficient of friction between the rod and the horizontal plane.

- A
- B
- C
- D

**Q10: **

A uniform ladder is resting in a vertical plane with its upper end against a smooth vertical wall and its lower one on a rough horizontal floor, where the coefficient of friction between the ladder and the floor is . The ladder is inclined to the horizontal at an angle measuring . Given that the ladder weighs 295 N and and has a length , find, in terms of , the maximum distance a man weighing 610 N can climb up the ladder without it slipping, rounding your answer to two decimal places.

- A
- B
- C
- D