1. During impending motion, the friction force’s line of action forms an angle ϕ with the normal. What happens to ϕ after motion starts?

A. ϕ increases to the angle of repose B. ϕ decreases to the angle of kinetic friction C. ϕ remains constant D. ϕ becomes zero

2. How does friction affect systems involving wedges used for adjusting heavy machinery?

A. It makes the system slippery and uncontrollable B. It allows wedges to remain stationary after being forced under loads C. It is negligible and often ignored D. It requires large forces to move the wedge

3. The normal force N and friction force F at a contact surface can be combined into a resultant force R. What does the angle between R and N represent?

A. Angle of applied load B. Angle of friction (ϕ) C. Angle of inclination D. Angle of repose

4. If a wedge remains in place under a load after being driven in, what role does friction play?

A. It reduces the load on the wedge B. It prevents the wedge from popping out, effectively locking it C. It increases the velocity of wedge movement D. It eliminates the need for an applied force

5. What happens to the friction force when motion actually begins?

A. It jumps from kinetic to static friction B. It remains at maximum static friction level C. It usually drops from maximum static friction to kinetic friction D. It becomes zero instantly

6. The force of kinetic friction (Fk) is generally:

A. Equal in magnitude to the maximum static friction force B. Independent of the normal force C. Constant during sliding velocity and less than maximum static friction D. Greater than the maximum static friction force

7. When a uniform bar of length l and mass m is acted upon by a force P, which factor influences the angle θ for equilibrium?

A. The coefficient of kinetic friction only B. The position of the center of mass and force direction C. The length of the bar alone D. The friction at supports only

8. How does the coefficient of kinetic friction (μk) typically compare to the coefficient of static friction (μs)?

A. μk is greater than μs B. μk is equal to μs C. μk is less than μs D. μk is zero when sliding starts

9. How is the principle of virtual work applied in systems involving frictionless connected rigid bodies?

A. By ignoring all force components B. By considering virtual displacements and calculating work done by forces and moments to solve for unknowns C. By equating kinetic energy to potential energy D. By assuming all friction forces are zero

10. What condition must be satisfied for the total virtual work δU in a system in equilibrium?

A. δU must be maximum B. δU must be positive C. δU must be zero for all virtual displacements D. δU must equal the kinetic energy change

11. If the polygon ABDC in a dump truck mechanism is a parallelogram, what is the implication for force transmission?

A. Forces and moments on AB and DC links cancel out B. Opposite sides are parallel and equal, simplifying torque analysis C. All forces act through the diagonal BD only D. The polygon cannot support a load if tilted

12. Why must the virtual displacement axes be measured from a fixed point on the free body diagram during virtual work analysis?

A. To align with the weight vector B. To simplify the calculation of deflections and rotations related to applied forces C. To eliminate reaction forces D. To increase the number of unknowns in the problem

13. When a force P is applied to a scissors linkage to maintain equilibrium at an angle θ, which force components are critical for analysis?

A. Vertical component only B. Horizontal component only C. Components parallel and perpendicular to the linkage arms D. Components normal to the friction surface

14. What occurs when the applied force exceeds the maximum static friction?

A. Friction increases infinitely B. The block remains stationary C. The block starts sliding and friction drops to kinetic friction D. The block moves and friction reaches maximum value

15. What is the significance of the angle of friction (ϕ) in analyzing frictional forces?

A. It defines the angle at which friction force becomes zero B. It relates the friction force to the normal force as tan ϕ = F/N C. It describes the angle of applied load D. It is always 90 degrees

16. The angle of repose is equal to which friction-related angle?

A. Angle of kinetic friction B. Angle of sliding friction C. Angle of static friction D. Angle of applied force

17. What type of friction is considered when bodies are in contact but not moving relative to each other?

A. Kinetic friction B. Static friction C. Fluid friction D. Rolling friction

18. When a block rests on a horizontal plane without movement, what balances its weight?

A. Frictional force B. Reaction normal force from the surface C. Applied horizontal force D. Gravity component

19. How can the magnitude of friction forces at multiple contact surfaces be reduced in analysis?

A. By assuming no friction at all B. By expressing friction forces in terms of their corresponding normal forces C. By considering only one surface's friction force D. By ignoring the coefficient of friction

20. When analyzing equilibrium using virtual work, why are virtual displacements considered imaginary and infinitesimal?

A. To simulate actual movement exactly B. To calculate potential energy changes C. To ensure first order differential quantities that do not physically occur D. To determine applied forces directly

21. What does the coefficient of static friction (μs) represent in the context of dry friction?

A. The minimum frictional force before movement starts B. The ratio of the normal force to the frictional force when sliding C. The proportionality constant relating maximum static friction force to the normal force D. The force required to keep a body moving at constant velocity

22. What is the angle of friction in relation to the normal and frictional forces acting on a body?

A. The angle between friction force and applied force B. The angle between the resultant reaction force and the normal to the surface C. The angle between the weight and the surface D. The angle of virtual displacement

23. What is a virtual displacement in the context of virtual work?

A. A real displacement under applied load B. A hypothetical infinitesimal movement assumed for analysis C. A permanent deformation of the structure D. The displacement after removing the load

24. What happens to the frictional force once a block begins to slide on a surface?

A. It immediately increases to a maximum value B. It remains equal to the applied force P C. It decreases from the maximum static friction force to the kinetic friction force D. It becomes zero

25. What is the primary reaction force at the contact surface of two smooth bodies in contact with no friction?

A. Tangential force to the surface B. Normal force perpendicular to the surface C. Frictional force parallel to the direction of motion D. Gravity

26. What defines whether a wedge is self-locking?

A. If the static friction coefficient is zero B. If the wedge angle is less than the angle of friction (ϕs) C. If the wedge is lubricated D. If the wedge weight is zero

27. When a block rests on an inclined plane and is on the verge of slipping, the angle of inclination at this point is called:

A. Angle of kinetic friction B. Angle of repose C. Angle of rotation D. Angle of deflection

28. When analyzing forces on a wedge, why are the friction forces F1 and F2 expressed in terms of their corresponding normal forces and coefficients of friction?

A. To reduce the number of unknown variables B. To increase complexity C. To avoid drawing free body diagrams D. Because friction does not depend on normal forces

29. When calculating virtual work, what sign convention is used for a force and displacement in the same direction?

A. Negative work B. Positive work C. Zero work D. It depends on the force magnitude

30. In the virtual work method for connected rigid bodies, why is it advantageous to select only one coordinate of displacement or rotation?

A. To increase redundancy B. To simplify the problem by expressing all virtual displacements in terms of that coordinate C. To ignore friction forces D. To avoid using free body diagrams

31. For a system of connected rigid bodies with one degree of freedom, what is the significance of defining coordinate axes parallel to the lines of action of forces?

A. It simplifies the calculation of moments B. It ensures correct direction of applied moments C. It allows calculation of virtual work along each coordinate axis D. It helps locate the center of mass

32. What is the ratio of maximum static friction force to the normal force called?

A. Coefficient of kinetic friction B. Coefficient of static friction C. Angle of repose D. Angle of kinetic friction

33. What is the unit of the coefficient of friction?

A. Newtons B. Meters C. It is dimensionless D. Degrees

34. If a uniform bar has length l and mass m, and is in equilibrium under a force P at an angle θ, what must be considered in the equilibrium analysis?

A. Only the mass of the bar B. Both length and mass for calculating moments and forces C. Neither mass nor length matter D. The bar length squared only

35. In the principle of virtual work for mechanical systems, what must be true for the virtual work done by all forces and moments at equilibrium?

A. It is maximized B. It is minimized C. It is equal to zero D. It is equal to the total external work input

36. What happens to the frictional force as an applied horizontal force increases up to the maximum static friction?

A. It decreases B. It remains constant C. It increases to balance the applied force D. It suddenly drops to zero

37. Why should position coordinate axes be aligned parallel to force lines of action in virtual work analysis?

A. To simplify calculations by directly relating displacements to forces B. To increase the number of unknowns C. To reduce the number of supports needed D. To eliminate friction forces

38. When a block rests on an inclined plane just before sliding, which law applies relating friction and normal forces?

A. F = μk N always B. F ≤ μs N with equality at impending motion C. N = 0 D. There is no friction at possible slip

39. What is dry friction primarily dependent on between two contacting surfaces?

A. Surface area in contact B. Speed of sliding C. Nature of the surfaces in contact D. Color of the surfaces

40. What factor is NOT considered in the calculation of friction force for dry friction between rigid bodies?

A. Nature of the contact surfaces B. Normal reaction force magnitude C. Sliding velocity D. Coefficient of friction

41. The principle of virtual work is effective for solving problems involving:

A. Only a single rigid body in motion B. Systems with infinite degrees of freedom C. Several connected rigid bodies with limited degrees of freedom D. Fluid flow problems

42. What condition must be satisfied for a block resting on a horizontal surface to remain in equilibrium when a horizontal force P is applied?

A. P must be less than or equal to the maximum static friction force B. P must exceed the weight of the block C. P must be perpendicular to the friction force D. P must equal the kinetic friction force

43. How is the friction force oriented relative to the motion or tendency of motion of a body?

A. Perpendicular to the surface B. Parallel and opposing the motion C. In the same direction as motion D. Normal to the motion

44. What is the purpose of drawing free body diagrams (FBDs) in friction and equilibrium problems?

A. To show deformation shapes B. To isolate bodies and show all forces acting to analyze equilibrium C. To draw artistic sketches of mechanical components D. To identify materials used

45. What determines the maximum angle α at which a steel wedge will not pop out of wood after being driven in?

A. The shape of the wedge only B. The coefficient of kinetic friction between wedge and wood C. The coefficient of static friction between wedge and wood D. The weight of the wedge

46. During equilibrium analysis using virtual work, if a force produces negative virtual work, what does this indicate about its direction relative to virtual displacement?

A. Force acts opposite the virtual displacement B. Force acts in the same direction as displacement C. Force has no influence on equilibrium D. Force is perpendicular to displacement

47. Which of the following is true about the coefficient of static friction μs?

A. It depends on the velocity of sliding B. It is usually higher than the coefficient of kinetic friction μk C. It always equals one D. It increases with surface area

48. In a linkage system undergoing virtual rotation δθ about a pivot, which forces typically contribute to virtual work?

A. Only reaction forces at fixed points B. Only applied loads and spring forces acting along displacements C. All forces except gravity D. Only frictional forces

49. In wedge systems, what effect does friction have on the wedge's functionality?

A. It always prevents motion B. Proper friction can lock the wedge in place after insertion C. Friction makes wedges ineffective D. Friction reduces the load the wedge can support

50. In terms of the principle of virtual work, what must be true about the total virtual work done by all forces on a body in equilibrium?

A. It is maximum B. It is equal to the external work applied C. It is zero for any virtual displacement D. It is positive for positive displacements only