9th Class Physics: Chapter 4 Turning Effect Of Forces Short Questions Answers

Resultant Vector: A resultant vector is a single vector that has the same effect as the combined effect of all the vectors to be added.

Torque: The turning effect of a force is called torque or moment of the force. It is determined by the product of force F and its moment arm L. It is denoted as τ. In SI units, the unit of torque is Newton-meter.

Centre of mass: Centre of mass of system is such a point where as applied force causes the system to move without rotation.

Centre of gravity: The centre of gravity of a body is defined as a point where the whole weight of the body appears at act vertically downward.

Differentiate the following:

(i) Like and unlike forces (ii) Torque and couple (iii) Stable and neutral equilibrium

(i) Like and unlike forces

Like forces:

• Like forces are also called like parallel force
• Like force are the forces that have the same direction to each other.
• A bag has a large number of apples in it, the weight of all the apples is acted vertically downward so these all forces are in same direction, called like forces.

Unlike forces:

• Unlike forces are also called unlike parallel forces.
• Unlike forces are the forces that are in the opposite direction to each other.
• An applies suspended by a string. The string is stretched by the weight of apple. Weight is acted downward but tension in the string is acted in upward direction. These are unlike forces.

(ii) Torque and Couple

Torque:

• The turning effect of a force is called torque or moment of the force.
• To produce a torque we need only one force at least.
• The torque is produced by force F and the moment arm.
• Torque by force is the product of force F and its moment arm.

Couple:

• A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.
• To produce a couple we need two unlike parallel forces at least.
• Torque of the couple = F x AB in this F represents the distance between two forces. The torque produced by a couple force F and F separated by the total distance AB that is the couple arm.
• The torque of a couple is given by the product of one of the two forces and the perpendicular distance between them.

(iii) Stable and neutral equilibrium

Stable equilibrium:

• A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.
• When a body is in stable equilibrium, its centre of gravity is at the lowest position. When it is tilted, its centre of gravity rises. It returns to its stable state by lowering its centre of gravity.
• A book placed on the table horizontally is an example of stable equilibrium.

Neutral Equilibrium:

• If a body remains in its new position when disturbed from its previous, it is said to be in a state of neutral equilibrium.
• In neutral equilibrium, the centre of gravity of the body remains at the same height, irrespective to its new position.
• The rolling ball is an example of neutral equilibrium.

Head to tail rule is a graphical method of vector addition. In this method according to a selected scale we draw all the forces according to their magnitude. Take any force as a first vector and the second force starts from the head of first vector by starting it with a tail so that tail of second vector coincides with the head of first vector. Simiarly, draw all the forces.

Such that head of previous vector coincides with tail of next vector. By drawing al the vectors in this manner, draw a resultant force, which starts from the tail of first force and its head coincides with the head of last force.

To resolve a force into its rectangular component, draw the resultant force according to its magnitude on the selected scale and required direction.

Then draw a perpendicular from the head of this resultant force to the x-axis and by joining make the y-component of the resultant force as below.

The F_y is the y-component of that vector and can be found as:

F_y = F sinθ

And F_x is the x-component of that vector and can be found as:

F_x = F cosθ

A body is said to be in equilibrium if it follows both conditions of equilibrium. A body is in equilibrium if net force acting on it is zero, and a body is said to be in equilibrium if the resultant torque acting on it is zero.

∑F = 0, or ∑F_y = 0, ∑F_x = 0

∑ τ = 0

The body is said to satisfy first condition for equilibrium if the resultant of all the forces acting on it is zero. Let ‘n’ number of forces F­₁ ­+F­₂ + F­₃+…… + F­_n = 0

Or  ∑F_n  = 0

The symbol ∑ is a Greek letter called sigma used for summation.

The first condition for equilibrium can also be stated in terms of x and y-components of the forces acting on the body as:

F­_1x ­+F­_2x + F­_3x+…… + F­_nx = 0

And F­_1y ­+F­_2y + F­_3y+…… + F­_ny = 0

Or ∑F_x = 0 and ∑F_y = 0

The first condition for equilibrium does not ensure that a body is in equilibrium. Consider a body pulled by the forces F_1­ and F₂, the two forces are equal but opposite to each other. These forces are not acted along the same as given in figure.

The first condition of equilibrium is although satisfied but the body has tendency to rotate. This situation demands another condition for equilibrium that is the second condition of equilibrium, a body satisfies second condition of equilibrium when the resultant torque acting on it zero. ∑ τ = 0

According to the second condition for equilibrium, a body satisfies second condition for equilibrium when the resultant torque action on it is zero. Mathematically; ∑ τ = 0

A paratrooper coming down with terminal velocity (constant velocity) is in equilibrium as all the forces acting on it is equal to zero, which satisfies the first condition of equilibrium.

Think of a body which is at rest but not in equilibrium.

There is not a single body in the universe which is at rest but not in equilibrium.

For a body is said to be in equilibrium it is necessary that the net force acting on a body is zero and the sum of all the torque acting on a body is zero. These two conditions cannot be satisfied if there is one force only. Because there is not any other force which nullify the effect of this force to keep the body in equilibrium and hence, this single force tends to move or rotate the body according to its point of application. So, if a single force is applied on a body, it could not be in equilibrium i.e

∑F ≠0

∑ τ ≠ 0

Vehicles are made heavy at the bottom and their height is kept to be minimum. This lowers their center of gravity and helps to increase their stability. Because to make them stable their center of mass must be kept as low as possible. Therefore height of vehicles is kept as low as possible.

Stable equilibrium:

• A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.
• When a body is in stable equilibrium, its centre of gravity is at the lowest position. When it is tilted, its centre of gravity rises. It returns to its stable state by lowering its centre of gravity.

For Example: Vehicles are made heavy at the bottom to keep its centre of gravity as low as possible.  A lower centre of gravity keeps it stable.

Unstable Equilibrium:

If a body does not return to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium.

The centre of gravity of the body is at its highest position in the state of unstable equilibrium.

For Example: Take a pencil and try to keep it in the vertical position on its tip. Wherever we leave it, the pencil topples over about its tip and falls down. In unstable equilibrium, a body may be made to stay only for a moment.

Neutral Equilibrium:

• If a body remains in its new position when disturbed from its previous, it is said to be in a state of neutral equilibrium.
• In neutral equilibrium, the centre of gravity of the body remains at the same height, irrespective to its new position.

For Example: When we roll a ball on a horizontal surface and leave it after displacing it from its previous position. It remains in its new position and does not return to its previous position.

Like forces:

• Like forces are also called like parallel force
• Like force are the forces that have the same direction to each other.
• A bag has a large number of apples in it, the weight of all the apples is acted vertically downward so these all forces are in same direction, called like forces.

Unlike forces:

• Unlike forces are also called unlike parallel forces.
• Unlike forces are the forces that are in the opposite direction to each other.
• An applies suspended by a string. The string is stretched by the weight of apple. Weight is acted downward but tension in the string is acted in upward direction. These are unlike forces.

A graphical method is used to find the resultant of two or more forces or vectors,  called the head to tail rule.

Head to tail rule method can be understood stepwise.

i. First select a suitable scale

ii. Draw the vectors of all the forces according to the scale; such as vectors A and B.

iii. Take any one of the vectors as first vector e.g., vector A.

iv. Draw next vector B such that its tail coincides with the head of the first vector A.

v. Draw the next vector for the third force (if any) with its tail coinciding with the head of the previous vector and so on.

vi. Draw a vector R as shown in the figure. The tail of vector R is at the tail of vector A, the first vector,  while its head is at the head of vector B, the last vector.

A resultant force is a single force that has the same effect as the combined effect of all the forces to be added.

If a force is formed from two mutually perpendicular components then such components are called its perpendicular components.

In ∆ABC

By Pythagoras’s theorem:

(Hyp.)² = (Base)² + (Perp.)²

(AC)² = (AB)² + (BC)²

(AC)² = (4)² + (3)²

(AC)² = 16 + 9 = 25

(AC) = 5

Thus, Length of hypotenuse is 5cm.

Perpendicular Components: If a force is formed from two mutually perpendicular components then such components then such components are called its perpendicular components.

Formula: To find their direction use the following formula:

θ = tan^-1

Sol. Scale

2N = 1cm

8N = 4cm

θ = 45^o

with x-axis

Rigid Body:

A rigid body is the one that is not deformed by force or forces acting on it.

Axis of rotation:

Consider a rigid body. As it rotates, its particles move in fixed circles. A fixed line that passed through the centers of these circles is called axis of rotation of the body.

Sol. Force = 150 N

Length off spanner = l = 10 cm

Torque = τ =?

We know that

τ = F x l

τ = 150 x 0.1

τ = 15 Nm

Rigid Body: A rigid body is the one that is not deformed by force or forces acting on it.

Torque: The turning effect of a force is called torque or moment of the force. It is determined by the product of the force F and its moment arm L. It is denoted as τ.

Formula: τ = L x F

Consider a rigid body. As it rotates, its particles move in fixed circles. A fixed line that passes through the centres of these circles is called axis of rotation of the body.

The perpendicular distance between the axis of rotation and the line of action of the force is called the moment arm is represented by distance (L)

Sol. Magnitude of Force = F = 100 N

= θ = 90^o

Magnitude arm = L = 10cm = 10 x 10^-2m

= 0.1m

Required: Find the torque produced by the force

= τ = ?

Formula: By using the basic relation;

Torque = Force x moment arm x sinθ

τ = F x L x sinθ

Solution: By substituting the values in above equation;

τ  = (100)(0.1) sin90^o

τ = (10)(1)                       sin90^o = 1

τ = 10 Nm

The torque produced by the force

Τ= 10Nm

Axis of Rotation:

Consider a rigid body. As it rotates, its particles move in fixed circles. A fixed line that passes through the centres of these circles is called axis of rotation of the body.

Moment Arm:

The perpendicular distance between the axis of rotation and the line of action of the force is called the moment arm of the force.

Moment: The turning effect of a force is called torque or moment of the force.

Principle of moments: A body is balanced if the sum of clockwise moments acting on the body is equal to the sum of anticlockwise moment on it.

Centre of mass of a system is such a point where an applied force causes the system to move without rotation.

The centre of gravity of a body is defined as a point where the whole weight of the body appears to act vertically downward.

Centre of mass: Centre of mass of a system is such a point where an applied force causes the system to move without rotation.

Centre of gravity: Centre of gravity of a body is defined as a point where the whole weight of the body appears to act vertically downward.

If a body remains in its new position when disturbed from its previous position, it is said to be in a state neutral equilibrium.

Torque:

• The turning effect of a force is called torque or moment of the force.
• To produce a torque we need only one force at least.
• The torque is produced by a force F and the moment arm.

Couple:

• A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.
• To produce a couple we need two unlike parallel forces at least.
• Torque of the couple = F x AB in this F represents force and AB represents the distance between two forces. The torque produced by a coupe force F and F separated by the total distance (AB), that is the couple arm.

Couple:

A couple is formed by two unlike parallel forces of the same magnitude but not along the same line.

Example: When a driver turns a vehicle, he applies forces that produce a torque. This torque turns the steering wheel. These forces act on opposite sides of the steering wheel as shown in figure. There forces are equal in magnitude but opposite in direction. These two forces form a couple.

Stable Equilibrium:

• A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.
• When a body is in stable equilibrium, its centre of gravity is at the lowest position. When it is tilted, its centre of gravity rises. It returns to its stable state by lowering its centre of gravity.
• A book placed on the table horizontally is an example of stable equilibrium.

Neutral Equilibrium:

• If a body remains in its new position when disturbed from its previous, it is said to be in a state of neutral equilibrium.
• In neutral equilibrium, the centre of gravity of the body remains at the same height, irrespective to its new position.
• The rolling ball is an example of neutral equilibrium.

According to the second condition for equilibrium, a body satisfies second condition for equilibrium when the resultant torque acting on it is zero. Mathematically;

∑ τ = 0

First condition of equilibrium:

A body is said to satisfy first condition for equilibrium if the resultant of all the forces acting on it is zero. i.e. ∑ F = 0

Second condition of equilibrium:

A body satisfies second condition of equilibrium when the resultant torque action on it is zero. i.e.  ∑ τ = 0

For a body is said to be in equilibrium it is necessary that the net force action on a body is zero and the sum of all the torques action on a body is zero. These two conditions cannot be satisfied if these is one force only. Because there is not any other force which nullify the effect of the force to keep the body in equilibrium and hence, this single force tends to move or rotate the body according to its point of application. So, if a single force is applied on a body, it could  not be in equilibrium i.e

∑ F ≠ 0, ∑ τ ≠0

Moment arm is represented by distance (L)

Stable equilibrium:

A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position. When a body is in stable equilibrium, its centre of gravity is at the lowest position. When it is tilted, its centre of gravity rises. It returns to its stable state by lowering its centre of gravity.

Stable Equilibrium:

A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.

In Stable equilibrium, the centre of gravity is at the lowest position.

Unstable Equilibrium:

If a body does not return to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium.

The centre of gravity of the body is at its highest position in the state of unstable equilibrium.