Q: Which of the following is a necessary condition for an object to be in static equilibrium?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Q: A $$10\,\mathrm{m}$$ long beam of mass $$50\,\mathrm{kg} is $$supported at its ends. A $$100\,\mathrm{kg}$$ load is placed $$2\,\mathrm{m}$$ from the left end. What is the upward force at the right support?

$$F_{right} = \frac{50 \times 9.8}{2} + \frac{100 \times 9.8 \times 8}{10}$$

Question 1

A uniform beam of length $$L$$ and mass $$m is $$supported horizontally by two supports at its ends. If a person of mass $$M$$ stands at a distance $$d$$ from the left end, what is the reaction force at the left support?

Accepted Answer

$$F_{left} = \frac{m g}{2} + \frac{M g (L - d)}{L}$$

Question 2

Which of the following is a necessary condition for an object to be in static equilibrium?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Question 3

A dentist applies two equal and opposite forces of $$2.0\,\mathrm{N} to a $$tooth in the $$x$$ and $$y$$ directions. What is the magnitude of the resultant force?

Accepted Answer

$$F_{res} = \sqrt{(2.0)^2$ + (2.0)^2$} = 2.8\,\mathrm{N}$$

Question 4

A $$200\,\mathrm{kg}$$ chandelier is suspended by two cables making angles of $$60^\circ$$ and $$30^\circ$$ with the ceiling. What is the tension in the cable at $$60^\circ$$?

Accepted Answer

$$T_1$$ = \frac{mg}{\sin 60^\circ + \sin 30^\circ}$$

Question 5

Which statement best describes the role of torque in static equilibrium?

Accepted Answer

The sum of all torques about any axis must be zero.

Question 6

A person stands on a uniform plank that is supported at both ends. If the person moves closer to the left support, what happens to the reaction force at the right support?

Accepted Answer

It decreases.

Question 7

Which of the following best explains why arches and domes are structurally strong?

Accepted Answer

They efficiently distribute compressive forces.

Question 8

A steel wire has a Young's modulus $$Y$$ and is stretched by a force $$F. If $$its original length is $$L$$ and its cross-sectional area is $$A$$, what is the extension $$\Delta L$$?

Accepted Answer

$$\Delta L = \frac{F L}{A Y}$$

Question 9

A bone fractures when the stress exceeds a certain value. If a force $$F is $$applied to a bone of cross-sectional area $$A$$, what is the stress?

Accepted Answer

$$\sigma = \frac{F}{A}$$

Question 10

A $$10\,\mathrm{m}$$ long beam of mass $$50\,\mathrm{kg} is $$supported at its ends. A $$100\,\mathrm{kg}$$ load is placed $$2\,\mathrm{m}$$ from the left end. What is the upward force at the right support?

Accepted Answer

$$F_{right} = \frac{50 	imes 9.8}{2} + \frac{100 	imes 9.8 	imes 8}{10}$$

Question 11

Which of the following is NOT a correct statement about the center of gravity?

Accepted Answer

It is always located at the geometric center of an object.

Question 12

A horizontal beam is in equilibrium under three forces: its weight $$W$$ acting at its center, an upward force $$F_A at $$the left end, and an upward force $$F_B at $$the right end. Which equation expresses the equilibrium of vertical forces?

Accepted Answer

$$F_A + F_B - W = 0$$

Question 13

If a force is applied at an angle $$	heta to a $$lever arm of length $$r$$, what is the torque produced about the pivot?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 14

A material obeys Hooke's Law up to a certain limit. What happens if the applied stress exceeds the elastic limit?

Accepted Answer

The material undergoes permanent deformation.

Question 15

Which of the following is a real-world application of static equilibrium principles?

Accepted Answer

Designing bridges to withstand loads without tipping or collapsing.

Question 16

A dome structure is preferred in architecture because:

Accepted Answer

It distributes forces efficiently, reducing the risk of fracture.

Question 17

A $$5\,\mathrm{m}$$ long uniform bar of mass $$20\,\mathrm{kg} is $$supported horizontally at one end and by a cable at the other end making a $$45^\circ$$ angle with the horizontal. What is the tension in the cable?

Accepted Answer

$$T = \frac{20 	imes 9.8 	imes 2.5}{5 \sin 45^\circ}$$

Question 18

Which of the following best describes the difference between stress and strain?

Accepted Answer

Stress is force per unit area; strain is the relative deformation.

Question 19

A stone arch bridge is able to support heavy loads primarily because:

Accepted Answer

The stones are compressed, not stretched, under load.

Static Equilibrium, Elasticity, and Fracture: Study Notes

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