Ch#4 : Turning Effect Of Force Flashcards
Learn about the resolution of forces , torque and equilibrium
What are like and unlike parallel forces?
Like Parallel Forces : are the forces are parallel to each other and have same direction.
Example : Weight of apples in a bag.
Unlike Parallel Forces : are the forces which are parallel to each other and have opposite direction.
Example : Tension and weight of a apple hanging on a string.
Causes the body to rotate if they arent acting along the same line.
How can forces be added? , Explain head to tail rule.
Force is a vector quantity , so it cant be added by ordinary arithmetic rules.
Resultant Force : A resultant force is a single force which has the same effect as all the forces to be added.
Forces can be added by the head to tail rule.
Head to Tail rule : A graphical method of vector addition that can be used to add two or more forces.
Explanation : Take any vector as a the first vector , e.g vector A. Next draw vector B such that the tail of B coincides with the head of A , similarly do this for any other vectors.
Next , draw vector R such that the tail coincides with the tail of the first vectoe and head of the last vector. Vector R gives the magnitude and direction of the resultant force.
Explain the resolution of a force.
Definition : Splitting up of a force into two mutually perpendicular components is called the resolution of that force
Consider a force F represented by line OA making angle 0 with x-axis.
Draw a perpendicular AB on x-axis.
According to the head to tail rule , OA is represented by AB + OB
OA = OB + AB
The components OA and OB and perpendicular to each other.They are called the perpendicular components of OA.OB represents the x-component Fx and AB represents the y-component Fy.
F = Fx + Fy
Fx and Fy can be found with trigonometric ratios.
Fx/F = cos0
Fx = F cos0
Fy/F = sin0 Fy = F sin0
Explain the determination of a force from its perpendicular components.
Consider Fx and Fy as the perpendicular components of a force F. Fx and Fy are represented by OP and PR respectively.
According to head to tail rule ,
OR = OP + PR
OP represents F , OP represents Fx and PR represents Fy
The magnitude of force F can be determined by using the right angled triangle POR.
F² = Fx² + Fy²
F = √Fx² + Fy²
The direction of the force along x axis is given by ,
tan0 = Fy/Fx
0 = tan- X Fy/Fx
Describe rigid body , axis of rotation , torque , line of action and moment arm of a force.
Rigid Body : A body that isnt deformed by force or forces
Axis of Rotation : Consider a rigid body rotating about a line , the the particles of the body move in circles with their centers lying on this line.This line is the acis of rotation of the body.
Torque : The turning effect of a force is called Torque.
Torque = F x L
SI Unit : Nm
Line of action : The line along which a force acts is called the line of action.
Moment arm : The perpendicular distance between the axis of rotation and line of action is called the moment arm. It is represented by L.
What are clockwise and anti clockwise moments? , Define the principle of moments.
Clockwise moment : The torque produced in the clockwise direction
Anti-clockwise moment : The torque produced in the anti-clockwise direction.
Principle of moments: A body is balanced if the sum of clockwise and anti clockwise moments acting on it are equal.
Differ between center of mass and gravity.
Centre of Mass : The point where an appied force causes the system to move without any rotation.The force doesnt produce any torque in the body.
Centre of Gravity : A point where the weight of a body appears to act vertically downwards is called the centre of gravity.
A body consists of a large number of particles. The earth attracts each particle with a force equal to its weight.These forces are almost parallel. The point where the resultant of these forces acts towards the centre of the earth is called the centre of gravity
How to find the centre of gravity of a Square , Rect , Hollow or Solid sphere , Triangle and Hollow Cylinder?.
The centre of gravity of a square or rect is the point of intersection of its diagonals.
The centre of gravity of a hollow or solid sphere is its centre.
The centre of gravity of a triangle is the intersection of its medians.
The centre of gravity of a solid or hollow cylinder is the mid point on its axis.
How to find the center of gravity of a thin irregular shaped lamina with a plumbline?
A simple method to find the centre of gravity of a bodg is to use a plumbline.A plumbline consists of a small metal bob attached to string. When the bob is suspended , it points vertically downwards due to its weight. The centre of gravity of the bob is below the point of suspension.
Take an irregular piece of cardboard with holes A , B and C near the edges. Fix a nail on a wall. Support the cardboard on the nail through on of the holes. The cardboard can freely swing around the hole.The cardboard will come to rest with the centre of gravity just below the nail. A vertical line can be located from the hole by using a plumbline located by a nail.Mark the line of the cardboard.Repeat this process from the other holes. The lines will intersect at point G. G is the centre of gravity of the irregular shaped thing lamina.
What is a couple?
Couple : A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.
A double arm spanner is used to open nuts.
Equal forces of magnitude F on the ends of the spanner in the opposite direction.These forces form a couple which turns the spanner about point O.Torque produced from a couple has the same direction. Total torque will be
Torque = F(L1 + L2) Torque = F L
What is equilibrium and what are the conditions for equilibrium?
Equilibrium : A body is said to be in equilibrium if no net force acts on it.
A body in equilibrium remains at rest or moves with uniform velocity.
First Condition of Equilibrium:
A body is said to satisfy the first condition of equilibrium if the resultant of all forces acting on it is ZERO. Let n number of forces F1 , F2 ,..Fn act on a body such that :
F1 + F2 +…+Fn = 0
∑F = 0
Symbol ∑ is a greek letter called Sigma meaning summation.
This condition can be stated in terms of x and y components of the forces acting on the body as:
∑Fx = 0
And ∑Fy = 0
Second Condition of Equilibrium :
The first condition of equilibrium doesnt ensure a body is in equilibrium. Consider a body on which two forces F1 and F2 parallel and opposite to each other are acting along the same line so the resultant is ZERO.According to first condition , they are in equilibrium. Now shift the position of the forces. The body still fulfills the first condition of equilibrium but has the tendency to rotate. So we need a second condition of a equilibrium. A body satisfies the second condition of equilibrium if the resultant torque acting on it is ZERO.
Mathematically ,
∑T = 0
What is stable , unstable and neutral equilibrium? , Give examples.
Stable Equilibrium : A body is said to be in stable equilibrium if it returns its previous position after a slight tilt.
Example : Consider a book on table. Tilt it slightly by lifting one of its edges. It returns to its previous position.
Untable Equilibrium : A body is said to be in unstable equilibrium if it doesnt returns its previous position after a slight tilt.
The centre of gravity is at its highest position in this state. A tilt cause the body to topple and its center of gravity moves to a lower position.
Example : Attempting to balance a pencil vertically
Neutral equilibrium : If a body remains in its new position after being distributed from its original position , it is in a state of neutral equilibrium.
In this equilibrium , all states in which a body is moved are stable. The centre gravity stayes at the same height.
Example : A ball , sphere , roller or egg
