Q: A uniform beam of length 6 m is supported at both ends and carries a point load of 18 kN at 2 m from the left support. What is the reaction force at the right support? Use equilibrium equations.

$$R_B = \frac{18 \times 4}{6} = 12\ \text{kN}$$

Q: A box of mass 60 kg rests on a horizontal surface with a coefficient of static friction $$\mu_s = 0.5. $$What is the minimum horizontal force required to start moving the box?

$$F = 0.5 \times 60 \times 9.81 = 294.3\ \text{N}$$

Q: A 40 kg crate is pushed across a floor with a coefficient of kinetic friction $$\mu_k = 0.3. $$What is the frictional force opposing the motion?

$$F = 0.3 \times 40 \times 9.81 = 117.72\ \text{N}$$

Q: A 70 kg person stands on a horizontal floor. If the coefficient of static friction is $$0.6$$, what is the maximum horizontal force that can be applied before the person starts to slide?

$$F_{max} = 0.6 \times 70 \times 9.81 = 411.18\ \text{N}$$

Q: A 50 kg box is on a rough surface ($$\mu_s = 0.4$$, $$\mu_k = 0.3). $$What is the minimum force required to keep the box moving at constant velocity?

$$F = 0.3 \times 50 \times 9.81 = 147.15\ \text{N}$$

Q: A simply supported beam of length 10 m carries a point load of 30 kN at 7 m from the left support. What is the reaction at the left support?

$$R_A = \frac{30 \times 3}{10} = 9\ \text{kN}$$

Question 1

A uniform beam of length 6 m is supported at both ends and carries a point load of 18 kN at 2 m from the left support. What is the reaction force at the right support? Use equilibrium equations.

Accepted Answer

$$R_B = \frac{18 	imes 4}{6} = 12\ 	ext{kN}$$

Question 2

In a truss, member AB is found to have a force of $$-8 kN $$using the method of joints. What does the negative sign indicate?

Accepted Answer

Member AB is in compression.

Question 3

A simply supported beam of length 8 m carries a uniformly distributed load of $$w = 5 kN/m. $$What is the shear force just to the left of the right support?

Accepted Answer

$$V = -20\ 	ext{kN}$$

Question 4

Which of the following best describes the internal force that acts perpendicular to the cross-section of a beam?

Accepted Answer

Shear force ($$V)$$

Question 5

A box of mass 60 kg rests on a horizontal surface with a coefficient of static friction $$\mu_s = 0.5. $$What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = 0.5 	imes 60 	imes 9.81 = 294.3\ 	ext{N}$$

Question 6

A beam is subjected to a point load at its center. Which of the following statements is true about the bending moment at the center?

Accepted Answer

It is maximum.

Question 7

A 40 kg crate is pushed across a floor with a coefficient of kinetic friction $$\mu_k = 0.3. $$What is the frictional force opposing the motion?

Accepted Answer

$$F = 0.3 	imes 40 	imes 9.81 = 117.72\ 	ext{N}$$

Question 8

Which equation must be satisfied for a rigid body to be in static equilibrium in two dimensions?

Accepted Answer

$$\sum F_x = 0$$, $$\sum F_y = 0$$, and $$\sum M = 0$$

Question 9

A truss is loaded such that joint C has two unknown member forces and one known external force. Which method is most efficient to solve for the unknowns at joint C?

Accepted Answer

Method of joints

Question 10

A beam is loaded as shown: a 10 kN point load at 2 m from the left end and a 20 kN point load at 5 m from the left end. If the beam is supported at both ends (A and B, 5 m apart), what is the reaction at support A?

Accepted Answer

$$A_y = 6\ 	ext{kN}$$

Question 11

Which of the following is true about the forces in a truss member if the calculated force is positive?

Accepted Answer

The member is in tension.

Question 12

A beam is subjected to a uniformly distributed load $$w$$ over its entire length $$L. $$What is the expression for the maximum bending moment at the center?

Accepted Answer

$$M_{max} = \frac{wL^2$}{8}$$

Question 13

A 70 kg person stands on a horizontal floor. If the coefficient of static friction is $$0.6$$, what is the maximum horizontal force that can be applied before the person starts to slide?

Accepted Answer

$$F_{max} = 0.6 	imes 70 	imes 9.81 = 411.18\ 	ext{N}$$

Question 14

Which of the following best describes the difference between static and kinetic friction?

Accepted Answer

Static friction prevents motion up to a maximum value; kinetic friction acts during motion.

Question 15

A beam is cut at a section to analyze internal forces. Which internal force is responsible for causing the beam to bend?

Accepted Answer

Bending moment ($$M)$$

Question 16

A 50 kg box is on a rough surface ($$\mu_s = 0.4$$, $$\mu_k = 0.3). $$What is the minimum force required to keep the box moving at constant velocity?

Accepted Answer

$$F = 0.3 	imes 50 	imes 9.81 = 147.15\ 	ext{N}$$

Question 17

Which of the following is NOT a condition for equilibrium of a rigid body in two dimensions?

Accepted Answer

$$\sum F_z = 0$$

Question 18

A simply supported beam of length 10 m carries a point load of 30 kN at 7 m from the left support. What is the reaction at the left support?

Accepted Answer

$$R_A = \frac{30 	imes 3}{10} = 9\ 	ext{kN}$$

Question 19

In a truss analysis, which method is most suitable for finding the force in a specific member located away from the supports?

Accepted Answer

Method of sections

Question 20

A beam is subjected to a shear force of 8 kN and a bending moment of 24 kN-m at a certain section. Which statement is correct?

Accepted Answer

The beam will experience both shear and bending at this section.

Statics and Mechanics: Equilibrium, Structures, Internal Forces, and Friction

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