Physics Class 9 Chapter 4 Turning Effect of Forces
TURNING EFFECTS OF FORCES
Q1. What are force diagrams? Define like and unlike parallel force with examples.
Ans. Force Diagrams:
In force diagrams, the objects on which force are shown is reduced to a dot at its centre and the force acting on the object are represented by arrows pointing away from it.
If we were to draw a force diagram of a book (object) placed at rest on table, we would reduce book to a dot and draw two arrows representing forces acting on it. There are two forces acting on a book, one is the weight of the book, pulling it downward and the other force is normal force due to the table pushing the book upward.
Both forces are equal in magnitude but opposite in direction. These two forces are an example of balanced force where they cancel out each other and the book (object) remains in state of equilibrium.
In case of free fall object:
In case of free-fall objects, the force due to gravity on the book is unbalanced and the book accelerates downward, in this case the force diagram of a free fall book (object).
Like parallel force:
Like parallel force are those forces which are parallel to each other and having the same direction. They may have same or different magnitude.
When we lift a box with double support we are applying like parallel force from each support. These forces may not equal but parallel and act in the same direction as shown in fig.
Unlike parallel forces:
Unlike parallel forces are those force which are parallel to each other but they are opposite in direction.
When we apply force with our both hands on steering wheel of a car to turn it. The force from one hand may be greater than other. Here, we are applying unlike parallel forces as shown in fig.
Q2. Explain the addition of forces, in connection with head to tail rules.
Ans. Addition of Forces:
Addition of forces is a process of obtaining a single force (Resultant force) which produces the same effect as produced by number of forces acting together.
Forces are vector quantities and may be added geometrically by drawing them to common scale and placing those head to tail.
The addition of forces is simple for parallel force. In case of like parallel forces, add the magnitude of vectors (forces) and in case of unlike parallel forces, subtract the magnitude of vectors.
Addition of Non – Parallel Forces:
When the forces are non-parallel that are acting at angle other than 0 o and 180o Then for addition of such vectors (forces), we apply a special method called Head to tail rule in order to find their resultant force (Vector)
Head to tail rule:
According to head to tail rule, we will get a resultant for e (vector) by drawing the representative lines of the given forces in such a way that the tail of first force vector joins with the head of last force vector.
A resultant force is the sum of two or more forces which is obtained by joining the tail of first force vector to the head of last one. It is represented by “FR”. This method of adding forces is known as “head to tail rule” of addition of forces.
Consider two persons pulling a cart such that their force vectors are drawn to same scale to calculate the net or resultant for e applying on a cart, the following steps must be followed to add the vectors by head to tail rule.
- Draw a first force vector “FA” which shows that the force exerted by first person on the cart and making an angle A with x – axis. Draw a second force “FB” which shows that the force exerted by second person on the cart and making an angle B with x – axis.
- Join the tail of second force vector “FB” with the head of first force vector (FA) in the given direction.
- Now, the net or resultant force “FR” can be obtained by joining the tail of first vector “FA” to the head of the last force vector “FB”.
Mathematically, the magnitude of resultant vector can be written as:
FR = FA + FB
This rule for vector addition can be extended to any number of forces.
Q3. Define moment of a force. Give its mathematical description and elaborate the factors on which it depends?
Ans: Torque or Moment of force:
The turning effect produced in a body about a fixed point due to applied force is called torque or moment of force.
Torque is the cause of changes in rotational motion and is similar to force, which causes changes in translational motion. For example, opening a door or tightening a nut with spanner etc. Torque may rotate an object in clock wise or anticlock wise direction.
Torque is equal to the product of applied force “F” and the moment arm “d” which is the perpendicular distance from the axis of rotation to the line of action of rotation. Mathematically, it can be written as:
Torque = Force × moment arm (perpendicular distance) or = F × d
Quantity and Unit:
Torque is a vector quantity and its S.I unit is “Newton meter (Nm)”
Factors Affecting Torque:
Torque depends upon the following two factors
1. Magnitude of force (F) 2. Moment arm or perpendicular distance (d)
1. Magnitude of Applied Force (F):
Torque is directly proportional to the force applied “F” which means greater is the magnitude of force, greater will be the torque produced. If the force is applied near the axis of rotation, moment arm will be small and turning effect will be poor.
But if the force is applied at the pivot point then it will cause no torque since the moment arm would be zero i-e d = 0
2. Moment Arm (d):
Moment arm plays an important role in producing torque and it is directly proportional to the torque. Greater is the moment arm, greater will be the torque produced by applying less effort and vice versa.
To open the door, force ‘F’ is applied at perpendicular distance “d” from the axis of rotation. By increasing the moment arm‘d’ or applied force ‘F’, torque ‘’ will also increases. So, the closer you are to the door hinges (i-e the smaller‘d’ is), the harder it is to push. That is why; the door’s handle is made at the maximum distance from the hinges.
Q4. What is resolution of forces? Explain with an example how force can be resolved into rectangular components.
Ans: RESOLUTION OF FORCES:
The process of splitting a force vector into two or more force vectors is called resolution of forces.
A vectors (Force) is resolved into two components which are mutually perpendicular to each other, such components are called rectangular components of a force vector i. e horizontal component and virtual component.
Consider a force vector ‘F’ which is represented by line making an angle with x-axis.
Resolution of force (F):
Tor solves the force vector into its y. So, represents two forces i-e ⃗ and components, from point draw a perpendicular PQ on axis ⃗ “P”. Suppose x
i. Force ‘OQ’ is along x-axis i-e x represents horizontal component.
ii. Force ‘QP’ is along y-axis i-e y represents vertical components.
By⃗ applying head to tail rule, we see that sum of vector ⃗x and ⃗x is equal to resultant force vector i-e F = Fx + Fy
Therefore, Fx and Fy are the rectangular components of force vector F.
For Finding Magnitude of Rectangular Components:
The magnitude of and can be determined by using trigonometric ratios. For Horizontal Component OPQ, we use the ratio cost in order to Now considering the right angle triangle find the value of Cosθ = Cosθ = :. OQ = FX , OP = F Cosθ =
By cross multiplication, we get For Vertical Component Fy: = Fcosθ —- (i)
To find the value of Fy, we use the ratio sin θ
:. QP = Fy, OP =F
By cross Multiplication, we get
Fy = F Sinθ ———- (ii)
So, we can calculate the magnitude of and components of force vector by using eq (i) and (ii) For finding magnitude of force �⃗:
If the values of rectangular components⃗ Fx and Fy of a force vector are known, we can determine the magnitude of Resultant force According to Pythagoras theorem (Hyp)2 = (Base)2 + (Perpendicular)2
Taking square √root 2 F = F2 = Fx2 + Fy2 on �both2 side:2 = 2 + +2
For Direction θ:
The direction (θ) of in right angle triangle OPQ is determined by using trigonometric tan θ = ratio of tanθ. tan θ = tan θ = θ = tan-1
Q5. What is Couple? Explain with examples.
Two equal and opposite parallel forces acting along different lines on a body is called a couple.
Couple does not produce any translational motion but only rotational motion. In other words, the resultant force of a couple is zero but the resultant of a couple is not zero. It is a pure moment. The shortest distance between two couple forces is called coplanar.
Consider an example of steering wheel gripped by two hands is often a couple. Each hands grips the wheel at points on opposite sides of the shaft. When both hands apply a force F1 and F that is equal in magnitude but opposite in direction, he wheel rotates.
So, a pure couple always consists of two opposite forces equal in magnitude. If both hands apply a force in same direction, the wheel will not rotate
Similarly, in our daily life, we come across many objects which work on the principle of couple. e.g.
- Exerting force on bicycle pedals
- Winding up the spring of a toy car
- Opening and closing the cap of a bottle
- Turning of a water tap etc.
Q6. Define equilibrium. Explain its types and state the two conditions of equilibrium
The state of a body in which under the action of several forces acting together, there is no change in translational motion as well as rotational motion is called equilibrium.
If there is no change in state of rest or of uniform motion of a body, the body is said to be in state of equilibrium.
Type of Equilibrium:
There are two type of equilibrium which are as follow.
- Static equilibrium
- Dynamic equilibrium
1. Static equilibrium:
When a body is at rest under the action of several forces acting together and several torques acting, the body is said be in static equilibrium
For example, a book is resting on the table and two forces are acting on it i-e weight of book and reaction force of table. Both forces are equal in magnitude but opposite in direction. So, the net force is zero and the book is said to be in state of static equilibrium.
2. Dynamic Equilibrium:
When a body is moving at uniform velocity under action of several forces acting together, the body is said to be in dynamic equilibrium.
The dynamic equilibrium is further divided into two types
- Dynamic Translational equilibrium
- Dynamic Rotational Equilibrium
1. Dynamic Translational Equilibrium:
When a body is moving with uniform linear velocity, the body is said to be in dynamic translational equilibrium.
For example, a paratrooper falling down with constant velocity is in state of dynamic translational equilibrium
2. Dynamic Rotational Equilibrium:
When a body is moving with uniform rotation, the body is said to be in dynamic rotational equilibrium.
For example, a Compact disk (CD) rotating in CD player with constant angular velocity is in state of dynamic rotational equilibrium.
Conditions of Equilibrium:
There are two conditions of equilibrium which are necessary for a body to be fulfilled
First Condition of Equilibrium:
When the sum of all the forces acting on the body is Zero, then first condition of
= F + F + F … … … equilibrium is satisfied net is the sum of force F, F, F … … … …. . F then
Or 2 3 n
net ∑ … . . +F
net = = 0
Where ∑ represents the sigma or summation.
Second Condition of Equilibrium:
When the sum of all the torques acting on the body is zero then the second condition of equilibrium is satisfied.
First condition is valid up to translational motion while the second condition is up to rotational motion. Thus, for complete equilibrium both the first and second conditions of equilibrium must be satisfied by a body.
Q7. State and explain principle of moments with example.
Ans. Principle of Moments:
For an object to be in equilibrium the sum of the clockwise torque taken about the pivot must be equal to the sum of anti – clock wise torque taken about the same pivot this principle is known as principle of moments.
I.e. sum of Anticlock wise Torque = Sum of Clock Wise Torque
1 = 2
Second condition of equilibrium is also called principle of moments.
In the given figure, a rod is balance about pivot. Here torque produced by “w1” and “w2” is anti-clockwise and torque produced by “w3” is clockwise.
Clockwise torque = Anti-clockwise torque
=+ (× 2) = (5 × 2) + (2 × 1) 12 = 12
Hence, there is only one clock wise moment about the turning point, but two anti-clock wise moments add up to balance it.
For second condition of equilibrium, the sum of Ʃ all these torques must be zero−.
+ Ʃ + = +
+ + =
Q8. What is centre of mass Or centre of gravity Explain how CM/CG can be determined? Is there any difference between CM and CG?
Ans: Centre of Mass (CM):
The centre of mass of the body is the point about which mass is equally distributed in all direction. It is denoted by “CM”.
The identification of this point is possible by applying a force at this point which will produce linear acceleration.
Center of Gravity (CG):
The Centre of gravity of the body is a point inside or outside a body at which whole weight of the body appears to act. It is denoted by “CG”
Everybody has a centre of mass (CM) where whole mass of a body is located and the CM is also the point at which the force of gravity is acting vertically downward i-e “CG”. For most of the time, these two points are lie at the same position in an object.
Determination of CG and CM for regular shaped bodies:
The centre of gravity “CG” and centre of mass “CM” of regular shaped bodies is located at the geometrical centre of the body. So the CG and CM of different symmetric bodies are shown in following table.
Name of Object Position of CM& Shapes of objects CG Circle Centre of circle CG Square or Intersection of 2 CG Rectangular plate diagonals CM 3 Triangular Plate Intersection of medians CG & CM Uniform rod Centre of rod CG & CM
Determination of CG and CM for irregular shaped bodies:
The CG or CM of irregular shaped bodies can be determined with the help of plumb line. If we take an irregular shaped object and make up a plumb line, then suspend it randomly from at least three different points and trace the plumb lines location. So, the point of intersection of all three plumb lines is the CG or CM of an object.
Difference between CG and CM:
The CG is based on weight of a body whereas the CM is based on mass of a body. Also, CG depends on the gravitational field whereas CM does not depend upon the gravitational field. So, when the gravitational field across an object is uniform, the centre of mass and centre of gravity are in exactly the same position.
However, near the surface of earth or on the surface of earth, the gravitational force is uniform; therefore CM and CG are present at the same point inside or outside a body. However, when gravitational field is non – uniform, the CM and CG does not lie at same point in an object. The CG will move closer to regions of the object in a stronger gravitational field, where as CM is unmoved.
Q9. Explain the stability of the objects with reference to position of centre of mass.
The stability of an object refers to the ability of an object to co e back in its original position after removing the force which was applied for its disturbance. Or Stability is a measure of how hard it is to displace on object or system from equilibrium
The degree of stability depends on how the position of centre of mass (CM) or centre of gravity (CG) of an object change when disturbed by some external force and how much it has the tendency to come back to its original position.
States of Equilibrium:
On the basis of stability of an object, here are three states of equilibrium which are as follow
- Stable Equilibrium
- Unstable Equilibrium
- Neutral Equilibrium
1. Stable Equilibrium:
When a body in equilibrium is slightly disturbed, its CM moves up and after removing external force, the CM of a body comes to its original position and regain its stability this state of equilibrium is call d stable equilibrium.
It is observed that if a book lifted from its edge, the CM of the book raised and when released, it comes back to its original position because the vertical line of action of weight passing through CM of body still falls inside the base and the torque caused by the weight of the body brings back the body to its original position.
Other examples of stable equilibrium are table, chair, box and brick lying on the floor.
2. Unstable Equilibrium:
When a body in equilibrium is slightly disturbed and its CM moves down and cannot come back to its original position after removing external force. This state of equilibrium is called unstable equilibrium.