9th Class Physics Chapter 4 Turning Effect of Forces Long Questions

Question 1

Explain the principle of moments with an example.

Accepted Answer

Statement Principle of moments: When a body is balanced, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point. Experiment Balance a metre rule on a wedge at its centre of gravity so that it is horizontal. Hang two weights w₁ and w₂ on one side at distances l₁ and l₂ from the wedge, and move a third weight w₃ on the other side until the rule balances again at distance l₃. Diagram Explanation w₁ and w₂ try to turn the rule anticlockwise; their moments are w₁ × l₁ and w₂ × l₂.; w₃ tries to turn it clockwise; its moment is w₃ × l₃.; When the rule is balanced: w₁l₁ + w₂l₂ = w₃l₃. Σ anticlockwise moments = Σ clockwise moments Example Anticlockwise: 2 × 20 + 1 × 40 = 80 N cm. Clockwise: w₃ × 30. w₃ = 80 ÷ 30 ≈ 2.67 N. w₃ ≈ 2.67 N Applications See-saws and beam balances.; Levers such as a crowbar, scissors and a wheelbarrow.; A tightrope walker's balancing stick. The principle of moments is the second condition of equilibrium (Στ = 0) written for a body that can turn about a pivot.

Question 2

Describe how you could determine the centre of gravity of an irregular-shaped lamina experimentally.

Accepted Answer

Principle A body hanging freely from a point comes to rest with its centre of gravity directly below the point of suspension, because only then does its weight have no turning effect. So G lies on the vertical line through the point of suspension. Apparatus Irregular cardboard sheet (lamina) with three small holes near its edge; Stand with a pin or nail; Plumb line (thread with a small weight); Pencil and ruler Method Hang the lamina on the pin through hole A so it can swing freely, and let it come to rest.; Hang the plumb line from the same pin in front of the lamina.; Mark two points along the plumb line and join them with a straight line.; Hang the lamina from hole B and draw the plumb line in the same way.; The point where the two lines cross is the centre of gravity G. Diagram Check and precautions Hang the lamina from a third hole: the third line should pass through the same point G.; The lamina and the plumb line must hang freely, not touching the stand.; Make the holes small and near the edge, far apart from each other. The centre of gravity is the point where the vertical lines from different points of suspension intersect.

Question 3

State and explain the conditions of equilibrium. Show that if two equal and opposite forces act at two different points of a body, the resultant force is zero but the resultant torque is not zero.

Accepted Answer

First condition of equilibrium Statement: The vector sum of all the external forces acting on a body is zero. ΣF = 0, that is ΣFx = 0 and ΣFy = 0 It ensures translational equilibrium: the body has no linear acceleration, so it stays at rest or moves with uniform velocity. Second condition of equilibrium Statement: The vector sum of all the torques acting on a body about any point is zero. Στ = 0 It ensures rotational equilibrium: the body has no angular acceleration, so it does not start to turn (or keeps turning steadily). Complete equilibrium A body is completely in equilibrium only if both conditions hold. A book lying on a table is an example. Equal and opposite forces at two different points Case (a): F₁ and F₂ are equal and opposite and act along the same line. ΣF = 0 and neither has a moment about the point where they act, so the body stays in equilibrium.; Case (b): F₁ and F₂ are equal and opposite but act along different lines, a distance d apart. Still ΣF = F − F = 0, so the first condition holds. But both forces turn the body the same way, so Στ = F × d ≠ 0 and the body rotates. The first condition alone is not enough: a couple satisfies ΣF = 0 but not Στ = 0, so a body acted on by a couple is not in equilibrium.

Question 4

How can the stability of an object be improved? Give a few examples to support your answer.

Accepted Answer

Meaning of stability A body is stable if it returns to its position after being tilted. It topples when the vertical line through its centre of gravity falls outside its base. Two ways to improve stability Lowering the centre of gravity, so the body must tilt much farther before the line from G leaves the base.; Widening the base, so the line from G has farther to go before it passes outside the base. Examples Low armchair, More stable than a tall stool: low centre of gravity; Loading a bus or truck, Heavy goods on the floor keep G low; luggage on the roof raises G and the bus can overturn on a sharp turn; Racing cars, Very low body and wheels wide apart, outside the main body; Balancing toys, G kept below the pivot; when tilted, G rises, so the toy swings back; Table lamps, pedestal fans, Heavy, wide base To make anything stable: keep its centre of gravity low and its base wide.

Question 5

What is torque? Explain the factors on which it depends, with examples. Write its formula and unit.

Accepted Answer

Definition Torque (moment of a force): The turning effect of a force, equal to the product of the force and its moment arm. τ = F × l Moment arm: The perpendicular distance from the axis of rotation to the line of action of the force. Diagram Factors on which torque depends Magnitude of the force: a larger force gives a larger torque. A tight nut needs a harder push.; Moment arm: the farther the line of action is from the axis, the larger the torque. A longer spanner opens a nut more easily; a door is easiest to open at the handle, far from the hinges.; Angle of the force: at an angle θ to the arm, τ = rF sin θ. It is largest at 90° and zero when the force points along the arm or through the axis. Sign of torque Anticlockwise, Positive; Clockwise, Negative Example τ = F × l = 300 × 1.2. 360 N m Pushing a door at its hinges does not open it, because the moment arm is zero.

Question 6

What is meant by resolution of a force? Find the rectangular components of a force, and explain how a force can be found from its components.

Accepted Answer

Definition Resolution of a force: Splitting a force into parts (components) that together have the same effect as the single force. Rectangular components: The two components at right angles to each other, along the x-axis and y-axis. Diagram Finding the components Draw F as OA at angle θ with the x-axis. From A drop a perpendicular AB onto the x-axis. OB is the x-component and BA is the y-component. In the right-angled triangle OBA: cos θ = OB ÷ OA = Fx ÷ F, so Fx = F cos θ.; sin θ = BA ÷ OA = Fy ÷ F, so Fy = F sin θ. Finding a force from its components By Pythagoras, OA² = OB² + BA²: F = √(Fx² + Fy²)     θ = tan⁻¹(Fy ÷ Fx) Example Fx = 200 cos 30° = 200 × 0.866 = 173.2 N. Fy = 200 sin 30° = 200 × 0.5 = 100 N. Check: √(173.2² + 100²) = √40 000 = 200 N. Fx = 173.2 N, Fy = 100 N

Question 7

What is a couple? Explain with examples, and show that the torque of a couple equals F × d.

Accepted Answer

Definition Couple: Two equal and opposite parallel forces acting at different points of a body along different lines of action. Couple arm: The perpendicular distance d between the lines of action of the two forces. Diagram Torque of a couple Take moments about the point midway between the two forces. Each force is d/2 from it.; Torque of each force = F × d/2, and both turn the body the same way.; Total torque = F × d/2 + F × d/2 = F × d. τ = F × d Effect of a couple Since the two forces are equal and opposite, the resultant force is zero and the body does not move along a line. But the torque F × d is not zero, so the body rotates. Examples Turning a steering wheel with both hands.; Opening a tap or a bottle cap.; Turning a key in a lock.; Winding a clock. A couple produces rotation only, never translation.

Question 8

What are the states of equilibrium? Explain each with examples in terms of the centre of gravity.

Accepted Answer

Introduction A body in equilibrium may react to a slight push in three ways. What happens depends on whether the push raises, lowers or does not change the height of its centre of gravity G. Diagram Stable equilibrium Definition: After a slight tilt the body comes back to its original position. Tilting raises G, and the weight turns the body back. Examples: a cone on its base, a book lying on a table, a ball in a bowl, a cylinder standing on its base. Unstable equilibrium Definition: After a slight tilt the body moves further away from its original position. Tilting lowers G, and the weight turns the body farther over. Examples: a cone balanced on its tip, a pencil on its point, a ball on top of a dome. Neutral equilibrium Definition: After being disturbed the body comes to rest in its new position. G stays at the same height, so the weight has no turning effect. Examples: a ball on a flat floor, a cylinder or cone lying on its curved side. Stable, Rises, Returns; Unstable, Falls, Topples; Neutral, Same height, Stays in the new position

Question 9

Define centripetal force. Explain it with examples and state the factors on which it depends.

Accepted Answer

Definition Centripetal force: The force that keeps a body moving in a circular path. It is always directed towards the centre of the circle. Fc = mv² ÷ r Diagram Explanation By Newton's first law a moving body goes straight unless a force acts. To move in a circle its direction must change all the time, so a force must keep pulling it towards the centre. This force is at right angles to the velocity, so it changes the direction but not the speed. Factors Mass m, Fc ∝ m: double the mass, double the force; Speed v, Fc ∝ v²: double the speed, four times the force; Radius r, Fc ∝ 1/r: half the radius, twice the force Examples Stone on a string: the tension in the string pulls the stone towards the hand.; Car on a curve: friction between tyres and road provides it.; Moon and satellites: the Earth's gravity provides it. If the force stops If the string breaks, the stone flies off along the tangent at that point, moving in a straight line. Fc = 0.5 × 4² ÷ 1. 8 N

Question 10

Explain the addition of forces by the head-to-tail rule, with the help of an example.

Accepted Answer

Introduction Forces are vectors: their directions matter, so they cannot simply be added as numbers. The head-to-tail rule adds them by drawing. Method Choose a suitable scale, for example 100 N = 1 cm.; Draw the first force to scale in its direction from a point O.; Draw the second force with its tail at the head of the first, then the third with its tail at the head of the second.; Join O (the first tail) to the head of the last force. This line is the resultant.; Measure its length (convert with the scale) and the angle it makes with the x-axis. Diagram Example (Solved Example 4.1) Draw 2 cm at 30°, then 3 cm at 45°, then 2.5 cm at 60°, head to tail. Join the first tail to the last head: it measures about 7.35 cm at 46° to the x-axis. Resultant = 7.35 × 100 ≈ 735 N. about 735 N at 46° The components confirm this: ΣFx = 510.3 N, ΣFy = 528.6 N, so F = √(510.3² + 528.6²) ≈ 735 N and θ ≈ 46°. Answers read off a rough drawing, such as 710 N at 43°, are a little out. The order in which the forces are drawn does not change the resultant.

Example	What makes it stable
Low armchair	More stable than a tall stool: low centre of gravity
Loading a bus or truck	Heavy goods on the floor keep G low; luggage on the roof raises G and the bus can overturn on a sharp turn
Racing cars	Very low body and wheels wide apart, outside the main body
Balancing toys	G kept below the pivot; when tilted, G rises, so the toy swings back
Table lamps, pedestal fans	Heavy, wide base

State	G on tilting	Result
Stable	Rises	Returns
Unstable	Falls	Topples
Neutral	Same height	Stays in the new position

Factor	Effect on Fc
Mass m	Fc ∝ m: double the mass, double the force
Speed v	Fc ∝ v²: double the speed, four times the force
Radius r	Fc ∝ 1/r: half the radius, twice the force

Turning	Sign
Anticlockwise	Positive
Clockwise	Negative

Long Questions with Answers

Set A: Textbook comprehensive questions 4 questions

Explain the principle of moments with an example.

Statement

Experiment

Diagram

Explanation

Example

Applications

Describe how you could determine the centre of gravity of an irregular-shaped lamina experimentally.

Principle

Apparatus

Method

Diagram

Check and precautions

State and explain the conditions of equilibrium. Show that if two equal and opposite forces act at two different points of a body, the resultant force is zero but the resultant torque is not zero.

First condition of equilibrium

Second condition of equilibrium

Complete equilibrium

Equal and opposite forces at two different points

How can the stability of an object be improved? Give a few examples to support your answer.

Meaning of stability

Two ways to improve stability

Examples

Set B: More important long questions 6 questions

What is torque? Explain the factors on which it depends, with examples. Write its formula and unit.

Definition

Diagram

Factors on which torque depends

Sign of torque

Example

What is meant by resolution of a force? Find the rectangular components of a force, and explain how a force can be found from its components.

Definition

Diagram

Finding the components

Finding a force from its components

Example

What is a couple? Explain with examples, and show that the torque of a couple equals F × d.

Definition

Diagram

Torque of a couple

Effect of a couple

Examples

What are the states of equilibrium? Explain each with examples in terms of the centre of gravity.

Introduction

Diagram

Stable equilibrium

Unstable equilibrium

Neutral equilibrium

Define centripetal force. Explain it with examples and state the factors on which it depends.

Definition

Diagram

Explanation

Factors

Examples

If the force stops

Explain the addition of forces by the head-to-tail rule, with the help of an example.

Introduction

Method

Diagram

Example (Solved Example 4.1)

The rest of Chapter 4

Long Questions from other Physics chapters