Equilibrium of Force system and Friction
- What are the conditions of equilibrium for concurrent forces and how is Lami's theorem used? In one line Concurrent coplanar forces are in equilibrium when the sums of their x and y components are both zero; for exactly three such fo... 1
- What are the conditions of equilibrium for parallel and general coplanar forces, and how are couples balanced? In one line A body under parallel or general coplanar forces is in equilibrium only when the net force is zero and the net moment about ever... 1
- What is a free body diagram and how do you draw it correctly for equilibrium problems? In one line A free body diagram (FBD) is a sketch of the body cut free from its surroundings, showing every external force and reaction acti... 1
- What are two-force and three-force bodies and how do they simplify rigid body equilibrium? In one line A rigid body in equilibrium under only two forces needs them equal, opposite and collinear; under three non-parallel forces, the... 1
- What are the types of beams, and what is the difference between a simple and a compound beam? In one line Beams are classified by their supports into simply supported, cantilever, overhanging, fixed, propped cantilever and continuous;... 1
- What are the types of supports on beams and what reactions does each provide? In one line A support provides a reaction for every motion it stops: a roller gives one force, a hinge gives two forces, and a fixed support... 1
- How are point loads, UDL, UVL and couples on a beam converted into equivalent forces? In one line Each distributed load is replaced by a single force equal to its area acting through the centroid of the load diagram; couples a... 1
- How do you determine support reactions of a simply supported or overhanging beam? In one line Draw the FBD, replace distributed loads by equivalent point loads, then use Σ M = 0 about one support and Σ F = 0 to get the rea... 1
- How do you find the reactions and fixing moment at the fixed end of a cantilever beam? In one line At a fixed end, the vertical and horizontal reactions balance the loads, and a fixing moment balances the total moment of all lo... 1
- What are the laws of static and kinetic friction and what is the coefficient of friction? In one line Friction is the resisting force along the contact surface that opposes relative motion, and its limiting value equals the coeffi... 1
- What are the angle of friction, angle of repose and cone of friction, and how are they related? In one line The angle of friction is the angle between the total reaction and the normal at limiting friction; the angle of repose is the st... 1
- How do you find the force needed to just move a body on a rough horizontal plane? In one line Write equilibrium along and perpendicular to the plane with friction at its limiting value μ N ; remember an inclined pull chang... 1
- How do you analyse a body on a rough inclined plane for impending motion up or down? In one line Resolve forces along and perpendicular to the incline and put friction at μ N acting opposite to the motion that is about to occ... 1
- How do you solve a ladder friction problem resting against a wall and a floor? In one line Treat the ladder as a rigid body with normal and friction forces at floor and wall, put friction at its limiting value where sli... 1
- Determine the tensions in the cords AB and BC for equilibrium of 30 kg block.[Figure: a 30 kg block hangs vertically from joint B. Cord BA goes up to the left to a support A and makes 30° with the horizontal at B; cord BC goes up to the right to a su… Given: W = 30 × 9.81 = 294.3 N. At joint B three concurrent forces act: T_AB (30° above horizontal, to the left), T_BC (40° above horizontal... 1
- A support block is acted upon by two forces as shown in fig. Knowing that the coefficient of friction between the block & the incline are \(\mu_s = 0.35\), \(\mu_k = 0.25\). Determine the force P required to prevent it from slipping down.[Figure: a b… Given: W = 800 N (vertical), P horizontal (towards the uphill side), θ = 25^° , μ_s = 0.35 (impending motion, so static coefficient is used)... 1
- Two spheres A and B weight 1000 N and 750 N. Determine the reaction at all contact points 1, 2, 3 and 4. \(r_A = 400\) mm, \(r_B = 300\) mm.[Figure: a container with a vertical wall on the left, a horizontal floor, and a right wall inclined at 60° to… Assumption (from the sketch): the lower sphere is B (r = 300 mm, 750 N) and the upper sphere is A (r = 400 mm, 1000 N). Contact points: 1 =... 1
- Determine the force P to cause the motion to impend. Take masses of the block A & B as 8 kg & 4 kg respectively and the coefficient of sliding friction as 0.3. The force P and the rope are parallel to the inclined plane. Assume frictionless pulley.[F… Given: m_A = 8 kg ( W_A = 78.48 N), m_B = 4 kg ( W_B = 39.24 N), μ = 0.3 , θ = 30^° . When P pulls A down the plane, the rope pulls B up the... 1
- For the beam loaded as shown in figure, Calculate the support reactions at A and B.[Figure: beam AF, 9 m long. A (left end) is a hinge support; B is a roller support 6 m from A. Dimensions from A: 2 m (point of 40 kN load and 20 kN·m couple), 1 m to… Note: the magnitude of P is not printed in the paper, so the reactions are obtained in terms of P (substitute the value of P if supplied). T... 1
- For the member shown in figure find the magnitude and direction of the resultant reaction at the hinged support A.[Figure: L-shaped member BAC. A is a hinge at the corner. AB is vertical, 3 m long, with its upper end B attached by a horizontal link t… The link at B can only exert a horizontal force R_B . Hinge A gives H_A and V_A . Σ M_A = 0:\ R_B × 3 = 30 × 4 ⇒ R_B = 40 N (acting to the l... 1
- Prove that angle of friction is equal to angle of repose. Angle of friction ( φ ): the angle between the resultant of the limiting friction F and the normal reaction N, and the normal reaction: tanφ... 1
- Determine the force P applied at 30° to the horizontal just necessary to start a roller having 50 cm radius over a 12 cm high obstruction, if the roller is of 100 kg mass. Also find the magnitude and direction of P when it is minimum.[Figure: roller… Given: W = 100 × 9.81 = 981 N, r = 50 cm, h = 12 cm. When the roller is just about to climb, the floor reaction becomes zero; the forces are... 1
- Find the force P required to pull block B shown in figure. Coefficient of friction between A and B is 0.3 and between B and floor is 0.25. Mass of A = 20 kg and B = 30 kg.[Figure: block B rests on a horizontal floor and block A rests on top of B. A s… Given: W_A = 20 × 9.81 = 196.2 N, W_B = 30 × 9.81 = 294.3 N, μ₁ = 0.3 (A–B), μ₂ = 0.25 (B–floor). A is held by the string; B is about to mov... 1
- For the beam loaded as shown in figure, Calculate the support reactions.[Figure: cantilever AB, 3 m long, fixed at A (left wall). A UDL of 10 kN/m acts over the first 2 m from A. At 2 m from A, a 20 kN force acts downward to the left, inclined at 60°… Loads: UDL resultant = 10 × 2 = 20 kN at 1 m from A. Inclined 20 kN: vertical component 20sin60^° = 17.32 kN (↓), horizontal component 20cos... 1