System of Forces
- What is the principle of transmissibility of a force and what are its limits? In one line A force acting on a rigid body can be slid anywhere along its own line of action without changing its external effect on the bod... 1
- How are force systems classified into coplanar, concurrent, parallel and non-coplanar types? In one line A force system is classified by whether the forces lie in one plane and whether their lines of action meet at a point or are par... 1
- How do you resolve a force into components and combine two forces into a resultant? In one line Resolution splits one force into perpendicular parts; composition combines several forces into one equivalent force called the r... 1
- How do you find the resultant of a coplanar concurrent force system by the method of resolution? In one line Add up all horizontal components and all vertical components separately; these two sums give the size and direction of the singl... 1
- How do you find the magnitude and position of the resultant of coplanar parallel forces? In one line The resultant of parallel forces equals their algebraic sum, and its position is found by making its moment equal to the total m... 1
- How is the resultant of a general coplanar (non-concurrent) force system found and located? In one line Find the resultant's magnitude and direction from Σ F_x and Σ F_y , then locate its line of action using Σ M about a point. Expl... 1
- What is the moment of a force about a point and how is its sign decided? In one line The moment of a force about a point is its turning effect, equal to the force times the perpendicular distance from the point to... 1
- What is a couple, what are its properties, and how is a force replaced by a force-couple system? In one line A couple is a pair of equal, opposite, parallel, non-collinear forces that produces pure rotation, and any force can be moved to... 1
- What does Varignon's theorem state and how is it proved and used? In one line Varignon's theorem says the moment of the resultant about any point equals the algebraic sum of the moments of its component for... 1
- How do you find the resultant of a non-coplanar concurrent (space) force system? In one line Write each force as a vector using unit vectors along its line, add the x, y and z components, and get the resultant and its dir... 1
- Resolve the force F = 900 N acting at B as shown in Fig. into parallel components at O and A.[Figure: horizontal bar OAB; O at the left end, A at 1 m from O, B at the right end, 2 m from A (OB = 3 m). A vertical downward force of 900 N acts at B.] Given: 900 N ( downarrow ) at B; OA = 1 m, AB = 2 m, OB = 3 m. Let the parallel (vertical) components be F_O at O and F_A at A, both assumed... 1
- A force of magnitude 50 kN is acting at point A(2,3,4) m towards point B(6,−2,−3) m. Find the components of this force along X, Y and Z axis. Position vector: AB = (6-2)hat i + (-2-3)hat j + (-3-4)hat k = 4hat i - 5hat j - 7hat k m |AB| = √(16 + 25 + 49) = √(90) = 9.487 m Unit vect... 1
- Determine the resultant of the following force system as shown in figure. Also locate its position w.r.t. O. Radius of circle is 2 m.[Figure: circle of radius 2 m, centre O, with horizontal and vertical centre lines. Four horizontal forces act at poi… Coordinates of points (O origin, x right, y up, r = 2 m): 150 N at (-2cos60^°, 2sin60^°) = (-1, 1.732) ; 90 N at (1.732, 1) ; 200 N at (1.73... 1
- A car is made to move by applying resultant force R = 2000 N along the x-axis. This resultant is developed due to two pulling forces \(F_1\) and \(F_2\) on two ropes as shown in figure. Determine the tension in individual ropes.[Figure: car with fron… Method: F₁ , F₂ and R form a force triangle (triangle law); apply the sine rule. The angle opposite R = 180° − 35° − 25° = 120°, so sin 120^... 1
- A force 30 N is acting at point P(3, 2, 1) m. The force makes 35° & 85° with x & y axes respectively. Express the force in vector form. Direction cosines satisfy cos²θ_x + cos²θ_y + cos²θ_z = 1 : cos²θ_z = 1 - cos² 35^° - cos² 85^° = 1 - 0.6710 - 0.0076 = 0.3214 ⇒ cosθ_z = 0.... 1
- A system of forces acting on a bell crank is as shown in fig. Determine the magnitude, direction and the point of application of the resultant w.r.t. O.[Figure: bell crank pivoted at O. A horizontal arm extends 300 mm to the left of O (two segments o… Axes: O origin, x right, y up; forces in N, distances in mm. ForcePoint (x, y) F_x F_y M_O = xF_y - yF_x 500 N(−300, 0)+250−433.01+129 904 1... 1