TURNING EFFECT OF FORCES Chapter #04 PHYSICS 9TH - Short / Detailed Question Answers

 PHYSICS 9TH - Short / Detailed Question Answers

TURNING EFFECT OF FORCES

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Q.1: Define force.

Ans: Force: Force is a push or pull which moves the objects. It can stop the objects. It also gives shape to the objects. It is a vector quantity. Therefore, it has a specific direction. It is measured in Newton (N).

Q.2: Define Parallel forces.

Ans: The parallel forces can be defined as, “when a number of forces act on a body and if their directions are parallel, they are called parallel forces.”

Q.3: What is meant by like and unlike forces?

Ans: 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. If many people are pushing a car to move it, all of these forces are called like parallel forces because these are acting along the same line.

Examples: “Consider two like parallel forces $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$acting on a body at “A” and “B”. Suppose $\overrightarrow{R}$is the resultant force of $\overrightarrow{F_1}$and $\overrightarrow{F_2}$, then $\overrightarrow{R} = \overrightarrow{F_1} + \overrightarrow{F_2}$.”

Unlike Parallel Forces: The forces that act along opposite directions are called unlike parallel forces.

Examples: For example, a ceiling fan suspended in a hook, through supporting rod. The forces acting on it are:

1. Weight of the fan acting vertically downwards, and
2. 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 as shown in the given figure, they can be responsible for the 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 equal and opposite forces directed at two different ends of the rod.

Examples:
“Consider two unlike parallel forces $\overrightarrow{F_1}$and $\overrightarrow{F_2}$ acting on a body at point “A” and “B”. Suppose $\overrightarrow{R}$is the resultant force of $\overrightarrow{F_1}$and $\overrightarrow{F_2}$. Here $F_1$ is greater than $F_2$.
$\overrightarrow{R} = \overrightarrow{F_1} - \overrightarrow{F_2}$”

Q.4: How can a force be represented?
Ans: Representation of a Force:
Force is a vector quantity. It has both magnitude (size) and direction. In diagrams, it is represented by a line segment with an arrowhead at one end to show its direction of action. Length of the line segment gives the magnitude of the force acting on an object.

Q.5: Define resultant of forces.
Ans: Resultant Force:
We need to add the forces acting on a body to get a single resultant force. A single force that has the same effect as the combined effect of the forces to be added is called the resultant force.

Q.6: Describe the methods of addition of 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):
(i) Graphical Method
(ii) Analytical Method

Q.7: Describe the graphical method of addition of forces. OR Which rule is used to find the resultant of more than two forces?

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

Head to Tail Rule: The given figure shows the head-to-tail rule of vector addition.

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 the first vector and draw the next vector in such a way that its tail coincides with the head of the previous. If the number of vectors is more than two, then continue the process until the last vector is reached.
Step 4: Use a straight line with an arrow pointed towards the last vector to join the tail of the first vector with the head of the last vector. This is the resultant vector.

Q.8: Define trigonometric ratios.

Ans: Trigonometric Ratios:
The ratio between any two sides of a right-angled triangle is given a specific name, and the ratio of any two sides of a right-angled triangle is called a trigonometric ratio.

There are six ratios in total, out of which three are main ratios and the 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.

$$\sin \theta = \frac{\text{perpendicular}}{\text{hypotenuse}} = \frac{AB}{BC}$$ $$\cos \theta = \frac{\text{base}}{\text{hypotenuse}} = \frac{AC}{BC}$$ $$\tan \theta = \frac{\text{perpendicular}}{\text{base}} = \frac{AB}{AC}$$

Q.9: What is meant by resolution of forces? By using trigonometric ratios find its horizontal and vertical 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 the resolution of vectors.

In other words, the process of splitting a vector into mutually perpendicular components is called the resolution of vectors. The given figure shows a force $F$ represented by a line segment $OA$, which makes an angle $\theta$ with the x-axis. Draw a perpendicular $AB$ on the x-axis from $A$. The components $OB = F_x$ and $BA = F_y$ are perpendicular to each other. They are called perpendicular components of $OA = F$. Therefore,

$$F = F_x + F_y$$

The trigonometric ratio can be used to find the magnitudes $F_x$ and $F_y$. In the right-angled triangle $\Delta OBA$,

$$\frac{F_x}{F} = \cos \theta \implies F_x = F \cos \theta \quad \text{(1)}$$

Also,

$$\frac{F_y}{F} = \sin \theta \implies F_y = F \sin \theta \quad \text{(2)}$$

Equations (1) and (2) give the perpendicular components respectively.

Q.10: How can we determine force from its perpendicular components? How the direction of a vector is obtained from its components?

Ans: Determination of Force from its Perpendicular Components:

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 as shown in the given figure.

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, $F = F_x + F_y$

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

$$(OR)^2 = (OP)^2 + (PR)^2 \quad \text{or} \quad F^2 = F_x^2 + F_y^2$$

Therefore,

$$F = \sqrt{F_x^2 + F_y^2}$$

The direction of $F$ with the x-axis is given by:

$$\tan \theta = \frac{PR}{OP} = \frac{F_y}{F_x}$$ $$\theta = \tan^{-1} \left(\frac{F_y}{F_x}\right)$$

Q.11: Define torque or moment. Write down its formula and units. List the factors on which moment of force depends.

Ans: Torque OR Moment of Force:

The turning effect of force is called moment of force or Torque.

Formula:

$$\text{Moment of force about a point} = \text{Force} \times \text{Perpendicular distance from point}$$ $$\vec{\tau} = \vec{F} \times \vec{d}$$

Units:

S.I unit of the torque or moment of force is Newton-meter (Nm).
Moments are described as clockwise or anticlockwise.

A door handle is fixed at the outer edge of the door so that it opens easily. A larger force would be required if the handle were fixed near the inner edge close to the hinge.

Similarly, it is easier to tighten or loosen a nut with a long spanner as compared to a short one.

Q.12: List the factors on which moment of force depends.

Ans: It depends upon:

(i) The magnitude of force.
(ii) The perpendicular distance of the point of application of force from the pivot or fulcrum.

Q.13: What is the principle of the moment?

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.

Q.14: How is the see-saw balanced?

Ans:
Two children playing on the see-saw. Fatima is sitting on the right side and Faheem on the left side of the pivot. When the clockwise turning effect of Fatima is equal to the anticlockwise turning effect of Faheem, then the 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 the principle of moments.

Q.15: Give three examples in which the principle of the moment is observed.

Ans:
Moments are everywhere. If we try to undo a bolt with our fingers, it is almost impossible, but if we add a spanner and 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.

The same principle applies when using a screwdriver to pry open a can of syrup or paint or closing the handles of a pair of scissors to slice through a sheet of card or a piece of string. The further away we apply the force from the pivot, the easier the task will become.

Moments don’t have to be on opposite sides of the pivot, either. A heavy load in a wheelbarrow is close to the wheel, while the handles are further away. This means that we need less force to lift the contents.

Some everyday examples where moments or the turning effect is observed are opening and closing doors and windows, nutcrackers, etc. Further, some examples of moments involve the application of levers, such as seesaws.

Q.16: Define centre of mass or centre of gravity.

Ans: Center of Mass OR Center 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.

Q.17: Where does the position of the center of gravity of a uniform rod lie?

Ans:
The centre of mass of a uniform meter rod is at its centre, and when supported at that point, it can be balanced as shown in figure (a).
If it is supported at any other point, it topples because the moment of its weight $W$ about the point of support is not zero, as shown in figure (b).

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Q.18: Write down the position of center of gravity of the following objects:

• (a) a uniform rod
• (b) a uniform square or rectangle sheet
• (c) a solid or hollow sphere
• (d) a uniform circular ring
• (e) a uniform circular disc
• (f) a uniform solid or hollow cylinder
• (g) a uniform triangular sheet

Ans:
The centre of gravity of regular shaped uniform objects is their geometrical centre.

S No	Name of the Object	Position of the Center of Gravity
(a)	A uniform rod	The center of gravity of the uniform rod is its midpoint.
(b)	Uniform square or rectangle sheet	The centre of gravity of a uniform square or rectangle sheet is the point of intersection of its diagonals.
(c)	A solid or hollow sphere	The center of gravity of a solid or hollow sphere is the center of the sphere.
(d)	A uniform circular ring	The center of gravity of a uniform circular ring is the center of the ring.

| (e) | A uniform circular disc | The center of gravity of a uniform circular disc is its center. | | (f) | A uniform solid or hollow cylinder | The center of gravity of a uniform solid or hollow cylinder is the midpoint on its axis. | | (g) | A uniform triangular sheet | The center of gravity of a uniform triangular sheet is the point of intersection of its medians. |

Q.19: How can you find the centre of gravity of an irregular shaped thin lamina or metal sheet or card sheet?

Ans: Center of Gravity of Irregular Shaped Thin Lamina

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 hole on a retort stand through a pin as shown in figure (a).

Step 3: Hang a plumb line or weight from the pin in front of the lamina as shown in figure (b).

Step 4: When the plumb line is steady, trace the line on the lamina.

Step 5: Repeat steps 2 to 4 for the second and third holes. The point of intersection of three lines is the position of the center of gravity.

​Q.20: What is a couple? Calculate the moment of the couple.

Ans: Couple:

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

Examples:

(i) When a boy riding the bicycle pushes the pedals, he exerts forces that produce a torque. This torque turns the toothed wheel making the rear wheel rotate. These forces act in opposite directions and form a couple.

(ii) Another example is the forces required to turn the 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 will cause it to rotate. A pair of forces like that is called a couple. A couple has a turning effect but does not cause an object to accelerate.

The Moment or Torque of the Couple:

The turning effect or moment of a couple is known as its torque. We can calculate the torque of the couple in the above figure by adding the moments of each force about the center O of the wheel.

$$\text{Torque of couple} = (F \times OP) + (F \times OQ)$$ $$= F \times (OP + OQ)$$ $$= F \times d$$

Torque of couple = one of the forces × perpendicular distance between the forces

Q.21: Write three necessary conditions for two forces to form a couple.

Ans: To form a couple, two forces must be:

(i) Equal in magnitude
(ii) Parallel, but opposite in direction
(iii) Separated by a distance

Q.22: Define equilibrium. What are the kinds of equilibrium?

Ans: Equilibrium:

When a body does not possess any acceleration, neither linear nor angular, then it is said to be in equilibrium. For example, a book lying on a table at rest, a paratrooper moving downwards with terminal velocity, a chair lift hanging on supporting ropes.

Kinds of Equilibrium: There are two kinds of equilibrium:

1. Static Equilibrium
2. Dynamic Equilibrium

Q.23: Define static and dynamic equilibrium.

Ans: Static Equilibrium:

A body at rest is said to be in static equilibrium.

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

Dynamic Equilibrium:

A moving object that does not possess any acceleration, neither linear nor angular, is said to be in dynamic equilibrium.

Examples: Uniform downward motion of stoolball through viscous liquid and jumping of the paratrooper from the helicopter are examples of dynamic equilibrium.

Q.24: Write down conditions of equilibrium.

Ans: Conditions for Equilibrium:

A body must satisfy certain conditions to be in equilibrium. There are two conditions for equilibrium.

First Condition for Equilibrium:

According to this condition for equilibrium, the sum of all forces acting on a body must be equal to zero. Suppose n number of forces, F₁, F₂, F₃, ..., Fₙ, are acting on a body, then according to the first condition of equilibrium:

F₁ + F₂ + F₃ + ... + Fₙ = 0 or ∑F = 0

The symbol (a Greek letter Sigma) is used for summation. The above equation is known as the first condition for equilibrium.

In terms of x and y components of the forces acting on the body, the first condition for the equilibrium can be expressed as:

F₁ₓ + F₂ₓ + F₃ₓ + ... + Fₙₓ = 0 and
F₁ᵧ + F₂ᵧ + F₃ᵧ + ... + Fₙᵧ = 0
or
∑Fₓ = 0 and ∑Fᵧ = 0

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

Second Condition for Equilibrium:

The first condition for equilibrium does not confirm that a body is in equilibrium because a body may have angular acceleration even though the first condition is satisfied.

For example, consider two forces F₁ and F₂ acting on a body as shown in figure (a). The two forces are equal and opposite to each other. The line of action of the two forces is the same, thus the resultant will be zero. The first condition for equilibrium is satisfied; hence we may think that the body is in equilibrium. However, if we change the position of the forces as shown in figure (b), now the body is not in equilibrium even though the first condition for equilibrium is still satisfied. This shows that there must be an additional condition for equilibrium to be satisfied for a body to be in equilibrium. This is called the second condition for equilibrium.

The sum of all clockwise and anticlockwise torques acting on a body is zero.

Mathematically,
τ = 0

Q.25: Write down the three states of equilibrium. Give examples of each.

Ans: States of Equilibrium:

There are three states of equilibrium:

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

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

(i) Stable Equilibrium:

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

A body is in stable equilibrium when:

• Its centre of gravity is at the lowest position.
• It is tilted, and its centre of gravity rises.
• It returns to a stable state by lowering its centre of gravity.

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

(ii) Unstable Equilibrium:

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

A body is in unstable equilibrium when:

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

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

(iii) Neutral Equilibrium:

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

A body is said to be in neutral equilibrium when:

• Its centre of gravity always remains above the point of contact.
• When it is displaced from its previous position, its centre of gravity remains at the same height.
• All the new states in which the body is moved are stable.

Example: Let us consider a ball placed on a horizontal surface, as shown in figure (a). It is in equilibrium. When it is displaced from its previous position, it remains in its new position, still in equilibrium, as shown in figure (b). This is called neutral equilibrium.

Q.26: Describe stability.

Ans: Stability:

In most situations, we are interested in maintaining stable equilibrium or balance, for example, in the design of structures, racing cars, and in working with the human body.

We consider a refrigerator: if it is tilted slightly (Fig b), it will return to its original position due to torque on it. But if it is tilted more (Fig. c), 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 one side of the pivot point, the torque pulls the refrigerator back onto its original base of support (Fig. b). 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 (Fig. c).

In general, a body whose centre of gravity is above its base of support will be stable if a vertical line projected downward from the centre of gravity falls within the base of support.

A sewing needle fixed in a cork. The forks are hung on the cork to balance it on the tip of the needle. The forks lower the center of mass of the system. If it is disturbed, it will return to its original position.

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