EQUILIBRIUM OF CONCURRENT FORCES

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• Q1: Define Concurrent Forces.
  Ans: Concurrent forces are forces whose lines of action meet at a single point.
• Q2: Define Non-Concurrent Forces.
  Ans: Non-concurrent forces are forces whose lines of action do not meet at a single common point.
• Q3: Define Vector Quantities. Name some.
  Ans: Vector quantities are physical quantities that have both magnitude and direction.
  Examples are:

  • ➔ Force
  • ➔ Velocity
  • ➔ Acceleration
  • ➔ Displacement
  • ➔ Momentum
• Q4: Define Scalar Quantities. Name some.
  Ans: Scalar quantities are physical quantities that have only magnitude and no direction.
  Examples are:

  • ➔ Mass
  • ➔ Time
  • ➔ Temperature
  • ➔ Energy
  • ➔ Distance
• Q5: Briefly explain Addition of Vectors.
  Ans: Vector addition is the process of finding the resultant vector by combining two or more vectors.
  It depends on both magnitude and direction and can be done using graphical or analytical methods.
• Q6: What is the Head and Tail Rule of Vector Addition?
  Ans: In the head and tail rule, the tail of one vector is placed at the head of another vector.
  The resultant vector is drawn from the tail of the first vector to the head of the last vector.
• Q7: What is the Law of Parallelogram of Vector Addition?
  Ans: If two vectors are represented by two adjacent sides of a parallelogram, then the diagonal passing through the common point represents the resultant vector.
• Q8: What is the Law of Triangle of Vector Addition?
  Ans: If two vectors are represented by two sides of a triangle taken in order, then the third side represents the resultant vector in opposite order.
• Q9: What is the Law of Polygon of Forces?
  Ans: If multiple forces acting on a body are represented by the sides of a polygon taken in order, then their resultant is given by the closing side of the polygon.
• Q10: What is the Resolution of Vectors?
  Ans: Resolution of vectors is the process of splitting a vector into two or more components along given directions.
• Q11: What are rectangular components of Vector?
  Ans: Rectangular components are the components of a vector along the x-axis and y-axis.
  They are given as:
  F_x = F cosθ
  F_y = F sinθ
• Q12: A force of 15N is acting at an angle of 30 degrees with x-axis. Find Fx and Fy.
  Ans: Given:
  Force (F) = 15 N
  Angle (θ) = 30°
  
  Formula:
  F_x = F cosθ
  F_y = F sinθ
  
  Calculation:
  F_x = 15 × cos30° = 15 × 0.866 = 12.99 N ≈ 13 N
  F_y = 15 × sin30° = 15 × 0.5 = 7.5 N
  
  Final Answer:
  F_x = 13 N
  F_y = 7.5 N
• Q13: What is Toggle Joint?
  Ans: A toggle joint is a mechanical device used to apply a large force at a small movement, commonly used in presses and crushers.
• Q14: State the mechanical advantage of Toggle Joint.
  Ans: The mechanical advantage of a toggle joint is very high when the joint is nearly straight, allowing a small effort to produce a large force.
• Q15: What is a Hanging Chain?
  Ans: A hanging chain is a flexible chain or cable that hangs under its own weight and forms a curve called a catenary.
• Q16: What is a Roof Truss?
  Ans: A roof truss is a framework of members arranged in triangular shapes to support the roof structure.
• Q17: Name the kinds of Truss.
  Ans: The kinds of trusses are:

  • ➔ Pratt Truss
  • ➔ Howe Truss
  • ➔ Warren Truss
  • ➔ Fink Truss
  • ➔ K Truss
  • ➔ Baltimore Truss
• Q18: Define Perfect Truss or Frame.
  Ans: A perfect truss is a truss that has just enough members to maintain its shape without deformation.
  Condition: m = 2j - 3
• Q19: Define Imperfect Frame or Truss.
  Ans: An imperfect truss does not satisfy the condition m = 2j - 3.
  It may be either deficient or redundant.
• Q20: Define Pratt Truss.
  Ans: Pratt truss is a type of truss in which diagonal members are in tension and vertical members are in compression.
• Q21: Define Howe Truss.
  Ans: Howe truss is a type of truss in which diagonal members are in compression and vertical members are in tension.
• Q22: Define Warren Truss.
  Ans: Warren truss consists of equilateral triangles and distributes load evenly without vertical members.
• Q23: Define Fink Truss.
  Ans: Fink truss is commonly used for roofs and has a pattern of V-shaped members for better load distribution.
• Q24: Define K Truss.
  Ans: K truss has members arranged in the shape of the letter K to reduce the length of compression members.
• Q25: Define Baltimore Truss.
  Ans: Baltimore truss is a modified Pratt truss with additional members to support heavy loads.
• Q26: What is Bow’s Notation?
  Ans: Bow’s notation is a method of labeling forces and members in a truss using letters for easy identification in graphical analysis.
• Q27: State the methods to solve frame structure.
  Ans: Methods to solve frame structures are:

  • ➔ Method of Joints
  • ➔ Method of Sections
  • ➔ Graphical Method
  • ➔ Analytical Method
• Q28: Briefly explain the method of sections to solve frame structure.
  Ans: In the method of sections, the truss is cut into two parts and equilibrium equations are applied to find forces in specific members.
• Q29: Briefly explain the Analytical method to solve frame structure.
  Ans: In the analytical method, mathematical equations of equilibrium are used to calculate unknown forces in members.
• Q30: Briefly explain the method of joints to solve frame structure.
  Ans: In the method of joints, each joint is considered separately and forces are calculated using equilibrium conditions.
• Q31: Briefly explain the Graphical method to solve frame structure.
  Ans: In the graphical method, forces are determined by drawing scaled force diagrams.
• Q32: What is a Crane? What is it used for?
  Ans: A crane is a machine used to lift and move heavy loads from one place to another.
  It is widely used in construction and industries.
• Q33: State the parts of Crane.
  Ans: Main parts of a crane are:

  • ➔ Mast
  • ➔ Jib
  • ➔ Pulley
  • ➔ Hook
  • ➔ Counterweight
• Q34: State the types of Cranes.
  Ans: Types of cranes are:

  • ➔ Jib Crane
  • ➔ Tower Crane
  • ➔ Mobile Crane
  • ➔ Overhead Crane
• Q35: Define Jib Crane.
  Ans: A jib crane is a type of crane that has a horizontal arm (jib) which supports a movable hoist.
• Q36: What is Crane Head?
  Ans: Crane head is the top part of a crane that supports pulleys and lifting mechanisms.
• Q37: State Lami’s Theorem.
  Ans: Lami’s theorem states that if three forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
  
  Formula:
  
  F₁/sinα = F₂/sinβ = F₃/sinγ