Turning Effect Of Forces - Physics For Class IX (Science Group) - Question Answers

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Physics For Class IX (Science Group)
UNIT 4: TURNING EFFECT OF FORCES
Questions Answers

Q.1: Define force?
Ans: FORCES:
Force is a push or pull. It moves the objects. It stops the objects. It gives shape to the objects.
Definition:

"Force is an agent which tends to change the state of an object."
OR
"Force is the agent that changes the state of rest or uniform motion of a body."

Nature: It is a vector quantity. Therefore, it has both magnitude (size) and specific direction. It is denoted by 'F'
Formula: 

F=ma

Where,
F is force applied on a body
m is mass of a body and
a is acceleration of a body

Unit: In SI system, unit of force is Newton (N) or kg-ms^-2.

Q.2: What do you mean by parallel forces? Define like and unlike parallel forces?
Ans: PARALLEL FORCES:
The parallel forces can be define as:

"When a number of forces act on a body, if their directions are parallel they are called parallel forces."

Thus lines of action of parallel forces are parallel to each other.

LIKE PARALLEL FORCES:

"The forces that act along the same direction are called like parallel forces."

Like parallel forces can add up to a single resultant force, therefore, can be replaced by a single force. In most cases, some or all of the forces are found acting in the same direction.
For example:

• Many people pushing a car to move it. All of them push it together in same direction. All of these forces are called like parallel forces because these are acting along same line.
  
  
• Consider two parallel force F₁ and F₂ acting on a body at "A" and "B". Suppose R is the resultant force of F₁ and F₂ then:
  "R = F₁ + F₂".

UNLIKE PARALLEL FORCES:

"The forces that act along opposite directions are called unlike parallel forces."

For example:

• A ceiling fan suspended in a hook through supporting rod. The forces acting on it are:
  (i) weight of the fan acting vertically downwards and
  (ii) tension in the supporting rod pulling it vertically upwards.
  These two forces are also parallel but opposite to each other and acting along the same line. Thus, these forces are called unlike parallel forces.
  These forces also add up to a single resultant force. But, when a pair of unlike forces do not act along the same line. They can be responsible for rotation of objects. Such unlike parallel forces cannot be replaced by a single resultant force and form a couple. A couple can only be balanced by an equal and opposite forces directed at the two different ends of the rod.
  
  
• Consider two parallel force F₁ and F₂ acting on a body at "A" and "B". Suppose R is the resultant force of F₁ and F₂. Here F₁ is greater than F₂ then:
  "R = F₁ - F₂".

Q.3: How can a force be represented?
Ans: Representation Of A Force:

• Force is a vector quantity. It has both magnitude (size) and specific direction.
• In diagrams it is represented by a line segment with an arrow-head at one end (⟶) to show its direction of action.
• Length of line segment gives the magnitude of the force on suitable scale.

Q.4: Define resultant of forces?
Ans: Resultant Of Force:
Wherever more than one force act on an object we need to add them to get a single resultant force. Thus it can be define as:

"Single force that has the same effect as the combined effect of the forces to be added is called resultant force."

OR

"The sum of the two or more forces is called the resultant of forces."

Q.5: Name the methods of addition of forces? which rule is used to find the resultant of more than two forces?
Ans: ADDITION OF FORCES:
Ordinary arithmetic rules cannot be used to add the forces. Two different methods are used for the addition of forces (i.e., in general addition of vectors):

1. Graphical Method
2. Analytical Method

Graphical Method:
The graphical method for addition of forces is called head to tail rule.
This method is used for addition of one-dimensional vector quantities. In this method head to tail rule of vector addition is used for the addition of forces.

Head to Tail Rule
Head to tail rule of vector addition consist of following steps:

• Step 1: Choose a suitable scale
• Step 2: Draw all the force vectors according to scale. Vectors A and B in this case.
• Step 3: Now take any vector as first vector and draw next vector in such a way that its tail coincides with head of the previous. If number of vectors is more than two then continue the process till last vector is reached.
• Step 4: Use a straight line with arrow pointed towards last vector to join the tail of first vector with the head of last vector. This is the resultant vector.

Q.6: Define trigonometric ratios?
Ans: Trigonometric Ratios:

• The ratio between any two sides of a right-angled triangle are given specific names.
• There are six ratios in total out of which three are main ratios and other three are their reciprocals.
• Three main ratios mostly used in physics are sine, cosine and tangent.
• Consider a right-angled triangle ΔACB having angle θ at C.
  BC = Hypotenuse
  AC = Base
  AB = Perpendicular

Q.7: What is meant by resolution of forces (vector)? By using trigonometric ratios find its horizontal and vertical component? OR Describe how a force (vector) is resolved into its perpendicular components?
Ans: RESOLUTION OF FORCES:
A force (vector) may be split into components usually perpendicular to each other; the components are called perpendicular components and the process is known as resolution of Vectors (Force).
In other words,

"The process of splitting of a vector into mutually perpendicular components is called resolution of vectors."

Components Of Force (Vector):

Consider a force (vector) F represented by a line segment OA which makes an angle θ with x-axis (OB). Draw a perpendicular AB on x-axis from A. In this way we get two components of a force.

1. Horizontal component OB
2. Vertical component BA

(i) Horizontal component OB:
The components OB which is along x-axis is called horizontal component of force and denoted by F_x.

(ii) Vertical component BA:
The components BA which is along y-axis is called vertical component of force and denoted by F_y.

The components OB = F_x and BA = F_y are perpendicular to each other. They are called the perpendicular components of OA = F.
Therefore,

F = F_x + F_y .................(i)

Magnitude Of Component F_x and F_y:
The trigonometric ratios can be used to find the magnitudes F_x and F_y. In right angled triangle ΔOBA.

Equations (ii) and (iii) give the perpendicular components respectively.

Q.8: Determine the magnitude and direction of a force from its perpendicular components.

OR

How can we determine force from its components? How direction of vector is obtained from its components?

OR

Describe addition of rectangular component of a vector and derive the expression for magnitude and direction of resultant vector?
Ans: Determination of Force (Vector) from its Perpendicular Components:
Addition of Rectangular Components of Vector:
Rectangular components of vector (components that are perpendicular to each other) can be joining together to form resultant or original vector.

Composition:
This is opposite to the process of resolution.

"If the perpendicular components of a force are known then the process of determining the force itself from the perpendicular components is called composition."

Suppose F_x and F_y are the perpendicular components of the force F and are represented by line segments OP and PR with arrowhead respectively.

Applying the head to tail rule:

OR = OP + PR

Here OR represents the force F whose x and y – components are F_x and F_y respectively.
Thus,

F = F_x + F_y

Magnitude Of A Force (Vector):
Consider right angle triangle OPR

• F_x = OP = Base
• F_y = PR = perpendicular
• F = OR = hypotenuse

In order to find the magnitude of F apply Pythagorean theorem to right angled triangle OPR i.e.,

(hyp)² = (b)² + (p)²

(OR)² = (OP)² + (PR)²

or F² = F_x² + F_y²

Therefore,

Direction Of Force (Vector):
The direction of F with x-axis is given by

Equation (i) and (ii) give the magnitude and direction of force (vector) respectively.

Q.9: Define Define moment of force or torque. Write down its formula and units? List the factors on which moment of force depends?
Ans: TORQUE OR MOMENT OF FORCE:
Definition: "The turning effect of force is called moment of force or Torque."
In other words,
"The product of the force and the moment arm of the force is equal to the torque."

Formula: Moment of force about a point = Force x Perpendicular distance from point.

or τ = F × d

Nature: Moments are described as clockwise or anticlockwise. Thus it is a vector quantity.
Unit: Depending on their direction, SI unit of the torque or moment of force is newton -metre (Nm).

Factors On Which Moment Of Force Depends:
It depends upon:

• The magnitude of force.
• The perpendicular distance of the point of application of force from the Pivot or fulcrum.

Q.10: Explain the turning effect of force by relating it to everyday life.

OR

Illustrate by describing a practical application of moment of force in the working of bottle opener, spanner, door/windows handle etc.
Ans: Examples Or Applications Of Moment Of Force Or Torque in our daily life:
Moments are everywhere, here are some examples:

Example No.1: Moment of force in the working of bottle opener.

• To remove the metal cap from a bottle with a bottle opener. We pull up on one end of the bottle opener, the bottle opener pivots on the middle of the metal cap and the lip of the opener forces the lid off.
• Turning moment works on the opener in three ways:
  The force of our hand as it pulls up on the handle of the opener.
  The force of the cap as it pulls down on the lip of the cap.
  The force of the corner of the mouth of bottle as it acts downwards on the opener at the pivot.
• As a result opener of bottle works as a lever. The lip of the opener will push up more with small effort on the lid, opening the bottle and the corner of the lid pulls down more (at the pivot).

Example No.2: Door / Windows Handle:
A door handle is fixed at the outer edge of the door so that it opens and closes easily. A larger force would be required if handle were fixed near the inner edge close to the hinge.

Example No.3: Spanner:
If we try to undo a bolt with our fingers is almost impossible. But if we add a spanner, suddenly it becomes very easy to turn. This is because we are increasing the distance between the force and the pivot and therefore we are increasing the turning moment.
Similarly, it is easier to tighten or loosen a nut with a long spanner as compared to short one.

Example 4: Load In A Wheelbarrow:
The further away we apply the force from the pivot, the easier the task will become. Moments do not have to be on opposite side of the pivot, either. A heavy load in a wheelbarrow is close to the wheel, the handle are further away. This mean that we need less effort (force) to lift the load.

Q.11: What is the principle of moment OR State the principle of moments.? Give example also.
Ans: PRINCIPLE OF MOMENT:
According to the principle of moments:

"The sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about that point."

OR

"A body is in equilibrium, if sum of the clockwise moments acting on a body is equal to the sum of the anticlockwise moments acting on the body."

Explanation: Seesaw
Two children playing on the see-saw. Girl is sitting on right side and boy on the left side of the pivot.
When the clockwise turning effect of girl is equal to the anticlockwise turning effect of boy, then see-saw balances. In this case they cannot swing.
When the sum of all the clockwise moments on a body is balanced by the sum of all the anticlockwise moments, this is known as principle of moments.

Examples:

• Seesaw
• Opening or closing of Door / Windows
• Spanner:
• Load in a wheelbarrow:
• Using a screwdriver to try to open a can of syrup or paint.
• Closing the handles of a pair of scissors to slice through a sheet of card or a piece of string.
• Nutcrackers

Q.12: Define center of mass or center of gravity? Where does the position of the center of gravity of a uniform rod lie?
Ans: CENTRE OF MASS OR CENTRE OF GRAVITY:
A body behaves as if its whole mass is concentrated at one point, called its centre of mass or centre of gravity, even though earth attracts every part of it.
In other words,

"The Center of mass or Center of gravity is a point where whole weight of the body acts vertically downward."

Center Of Gravity Of A Uniform Rod:
The centre of mass of a uniform metre rod is at its centre and when supported at that point, it can be balanced, if the fulcrum (pivot) is placed to support it at its center. If it is supported at any other point it topples (overbalance and fall) because the moment of its weight W about the point of support is not zero at that point.

Q.13: Determine the position of center of mass/gravity of regularly and irregularly shaped objects?
Ans: Center of Gravity of Some Regular Shaped objects:
The Center of gravity of regular shaped uniform objects is their geometrical Center.

• A Uniform Rod: The Center of gravity of uniform rod is its midpoint.
• A Uniform Square Or Rectangular Sheet: The Center of gravity of uniform square or a rectangular sheet is the point of intersection of its diagonals.
• A Solid Or Hollow Sphere: The Center of gravity of solid or hollow sphere is the Center of the sphere.

• A Uniform Circular Ring: The Center of gravity of uniform circular ring is the Center of ring.
• A Uniform Circular Disc: The Center of gravity of uniform circular disc is its Center. (Note: Figure is same as solid or hollow sphere)
• A Uniform Solid Or Hollow Cylinder: The Center of gravity of a uniform solid or hollow cylinder is the mid-point on its axis.
• A Uniform Triangular Sheet: The Center of gravity of a uniform triangular sheet is the point of intersection of its medians.

Center of Gravity of Irregular Shaped:
Thin Lamina Or Metal Sheet Or Card Sheet:

• Step 1: Make three small holes near the edges of the lamina farther apart from each other.
• Step 2: Suspend the lamina freely from one whole on retort stand through a pin.
• Step 3: Hang a plumb line or weight from the pin in front of the lamina.
• Step 4: When the plumb line is steady, trace the line on the lamina.
• Step 5: Repeat steps 2 to 4 for second and third hole. The point of intersection of three lines is the position of Center of gravity.

Q.14: What is couple with examples? Define couple as a pair of forces tending to produce rotation? Also calculate the moment of the couple Or Prove that the couple has the same moments about all points?
Ans: COUPLE:

"Two unlike parallel forces of the same magnitude but not acting along the same line form a couple."

OR

"Two equal and opposite forces acting along different lines of action form a couple."

Couple As A Pair Of Forces Tending To Produce Rotation:
The pair forces will cause a body to rotate. Such a pair of forces are called couple. A couple has turning effect but does not cause an object to accelerate.

Necessary Conditions:
To form a couple, two forces must be:

• Equal in magnitude
• Parallel, but opposite in direction
• Separated by a distanced.

The Moment Or Torque Of The Couple:
The turning effect or moment of a couple is known as its torque.
Consider the forces required to turn a circular body e.g. wheel of an object. The two equal and opposite forces (unlike parallel forces) balance, so the wheel will not move up, down or sideways. However, the wheel is not in equilibrium. The pair forces cause it to rotate.
Mathematically,
We can calculate the torque of the couple by two unlike parallel forces action on a wheel. By adding the moments of each force about the Center O of the wheel:
Torque of couple

= (F x OP) + (F x OQ)

= F x (OP + OQ)

= F x d .. (i)

Thus,

Torque of couple = one of the forces x perpendicular distance between the forces.

Example:
1. The role of couple in the steering wheels:
The forces required to turn steering wheel of a car. The two equal and opposite forces balance, so the wheel will not move up, down or sideways. However, the wheel is not in equilibrium. The pair forces cause it to rotate.

2. The role of couple in Bicycle pedals:
When a boy riding the bicycle pushes the pedals, he exerts forces that produces a torque. This torque turns the toothed wheel making the rear wheel to rotate. These forces act in opposite direction and form a couple.

Q.15: Define equilibrium? What are the kinds of equilibrium or Classify its types by quoting examples from everyday life?
Ans: EQUILIBRIUM:
When a body does not possess any acceleration neither linear nor angular it is said to be in equilibrium. For example:

• A book lying on table in rest.
• A paratrooper moving downwards with terminal velocity.
• A chair lift hanging on supporting ropes.

TYPES OR KIND OF EQUILIBRIUM:
There are two types of equilibrium.

1. Static Equilibrium
2. Dynamic Equilibrium

1. Static Equilibrium
A body at rest is said to be in static equilibrium.
Example:

• A wall hanging,
• Buildings, bridges or any object lying in rest on the ground are some examples of static equilibrium.

2. Dynamic Equilibrium:
A moving object that does not possess any acceleration neither linear nor angular is said to be in dynamic equilibrium.
For example:

• Uniform downward motion of steel ball through viscous liquid and
• Jumping of the paratrooper from the Helicopter.

Q.16: Write down conditions for equilibrium? OR State the two conditions for equilibrium of a body?
Ans: CONDITIONS FOR EQUILIBRIUM:
A body must satisfy certain conditions to be in equilibrium. There are two conditions for equilibrium:

1. First Condition for Equilibrium
According to this condition for equilibrium:

"Sum of the all forces acting on a body must be equal to zero."

OR

"First condition for equilibrium is satisfied if net force acting on a body is zero."

Explanation:
Consider two forces F₁ and F₂ are acting on a body. The two forces are equal and opposite to each other. The line of action of two forces is same (i.e. on the same plane), thus resultant will be zero. The first condition for equilibrium is satisfied, hence we may think that the body is in equilibrium.

Mathematically:
Suppose n number of forces F₁ , F₂ , F₃ , ………., F_n are acting on a body then according to first condition of equilibrium:

F₁ + F₂ + F₃ + ……… + F_n = 0 or

ΣF = 0 ............ (i)

The symbol Σ ( a Greek Letter Sigma) is used for summation. Equation (i) is known as first condition for equilibrium.
In terms of x and y components of the forces acting on the body first condition for the equilibrium can be expressed as:

F _1x + F_2x + F_3x + ……… + F_nx = 0 and

F_1y + F_2y + F_3y + ………. + F_ny = 0 or

ΣF_x = 0 ............. (ii)

ΣF_y = 0 ............. (iii)

Example:

• A basket of apples resting on the table or
• A clock hanging on the wall
  are at rest and hence satisfy first condition for equilibrium.
• A paratrooper moving down with terminal velocity also satisfies first condition for equilibrium.

2. Second Condition For Equilibrium:

"Second condition for equilibrium is satisfied if sum of clockwise torques acting on a body is equal to the sum of the anticlockwise torques."

Explanation:
First condition for the equilibrium does not confirm that a body is in equilibrium because a body may have angular acceleration even though first condition is satisfied. However, if we change the position of the forces that are not lie on the same plane. Now the body is not in equilibrium even though first condition for equilibrium is still satisfied. It is because the body has the tendency to rotate. This shows that there must be an additional condition for equilibrium to be satisfied for a body to be in equilibrium. This is called second condition for equilibrium. when the resultant torque acting on it is zero.

Mathematically:
Sum of all clockwise and anticlockwise torques acting on a body is zero.

Σ𝜏 = 0 ............... (iv)

Example:

• The force applying on the steering of the car
• Couple
• Children playing on the sea saw

Q.17: Describe the states of equilibrium and classify them with common examples. OR List states of equilibrium?
Ans: STATES OF EQUILIBRIUM:
There are three states of equilibrium:

1. Stable equilibrium
2. Unstable equilibrium and
3. Neutral equilibrium

A body may be in one of the above states of equilibrium.

Stable Equilibrium:

"A body is in stable equilibrium if when slightly displaced and then released it returns to its previous position."

Necessary Conditions For Stable Equilibrium:
A body is in stable equilibrium when:

• Its Centre of gravity is at lowest position
• When it is tilted its Centre of gravity rises
• It returns back to stable state by lowering its Centre of gravity

Thus, A body remains in stable state of equilibrium as long as its Centre of gravity acts through the base of the body.

Example:
Suppose a box is lying on the table. It is in equilibrium. Tilt the box slightly about its one edge. on releasing it returns back to its original position. This state of body is known as stable equilibrium.

2. Unstable Equilibrium:

A body is said to be in unstable equilibrium when slightly tilted does not return back to its previous position.

Necessary Conditions For Unstable Equilibrium:
A body is in unstable equilibrium when:

• Its Centre of gravity is at highest position
• When it is tilted its Centre of gravity is lowered
• Its previous position cannot be restored by raising its.

Example:
Take a paper cone and try to keep it in vertical position on its vertex. it topples down on releasing. This state of body is known as unstable equilibrium.

Neutral Equilibrium:

A body is said to be in neutral equilibrium when displaced from previous position remains in equilibrium in new position.

Necessary Conditions For Unstable Equilibrium:
A body said to be in neutral equilibrium when:
Its Center of gravity always remains above the point of contact.
When it is displaced from its previous position its Centre of gravity remains at same height.
All the new states in which body is moved are the stable states.

Example:
Consider a ball placed on a horizontal surface. It is in equilibrium. When it is displaced from its previous position it remains in its new position still in equilibrium. This is called neutral equilibrium.

Q.18: What is meant by stability? Explain effect of the position of the Centre of mass or center of gravity on the stability of simple objects.
Ans: STABILITY:

"Stability refers to the ability of a body to restore to its original static equilibrium, after it has been slightly displaced."

In general,

"A body whose center of gravity is above its base of support will be stable if a vertical line projected downward from the center of gravity falls within base of support."

Example:
Effect Of The Position Of The Centre Of Mass (Center Of Gravity) On The Stability:
(i) Refrigerator:
Consider a refrigerator, if it is tilted slightly it will return back to its original position due to torque on it. But if it is tilted more, it will fall down. The critical point is reached when the centre of gravity shifts from one side of the pivot point to the other.
When the centre of gravity is on the one side of the pivot point, the torque pulls the refrigerator back onto its original base of support. If the refrigerator is tilted further, the centre of gravity crosses onto the other side of the pivot point and the torque causes the refrigerator to topple.

(ii) Sewing Needle Fixed In A Cork:
A sewing needle fixed in a cork. The forks are hanged on the cork to balance it on the tip of the needle. The forks lower the centre of mass of the system. If it is disturbed will return back to original position.

(iii) Perched Parrot:
A perched parrot. It is made heavy at tail which lowers its centre of gravity. It can keep itself upright when tilted. In general, larger the base and lower the centre of gravity, more stable the body will be.

(iv) Sport Car:
The sports cars are made heavy at bottom which lowers the Center of mass and hence increases the stability.

Q.19: Why does a man carry a long beam, while walking on tight rope?
Ans: A man walking on tight rope carries a long beam which helps him to maintain balance by increasing their torque or moment of inertia and lowering his center of mass or the center of gravity. This help in maintaining stability and  resist to rotating and falling while walking over the narrow rope.