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Physics For Class IX (Science Group)
UNIT 4: TURNING EFFECT OF FORCES
Self Assessment and Test book Exercise
SELF ASSESSMENT QUESTIONS
Q.1: 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. 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.2: Differentiate like and unlike forces using examples.
Ans: Difference Between Like And Unlike Forces:
| S.No | LIKE PARALLEL FORCES | UNLIKE PARALLEL FORCES |
|---|---|---|
| 1. | The forces that act along the same direction are called like parallel forces. | The forces that act along opposite directions are called unlike parallel forces. |
| 2. | Like parallel forces can add up to a single resultant force, therefore, can be replaced by a single force. | 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. |
| 3. | 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". | 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". |
| 4. | 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. | 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. |
Q.3: Define resultant of a 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."
Ans: Graphical Method:
The graphical method for addition of forces is called head to tail rule, because in this method head to tail rule of vector addition is used for the addition of forces.
This method is used for addition of one-dimensional vector quantities and to find the resultant of more than two 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.5: What is meant by resolution of forces?
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."
Q.6: How the direction of a vector is obtained from its components?
Ans:Direction Of Force (Vector):
Consider right angle triangle OPR
- Fx = OP = Base
- Fy = PR = perpendicular
- F = OR = hypotenuse
Suppose Fx and Fy are the perpendicular components of the vector F and are represented by line segments OP and PR with arrowhead respectively.
The direction of vector (F) with x-axis is given by
Q.7: List the factors on which moment of force depends.
Ans: 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.8: What will be moment of force? When 500 N force is applied on a 40 cm long spanner to tighten a nut.
Solution:
Data:
- F = 500 N
- L = 40 cm = 40/100 = 0.40 m
- τ = ?
Formula:
τ = F × L
Calculation:
τ = 500 × 0.40 = 200 Nm Ans.
Ans: Thus, moment of force will be 200 Nm.
Q.9: How is the see- saw balanced?
Ans: See-Saw Balanced Due To Principle Of Moment:
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.
Q.10: Give three examples in which principle of moment is observed.
Ans: Examples Of Principle Of Moment:
1. Moments Acting On A Seesaw:
Two children playing on the see-saw. Girl is sitting on right side and boy on the left side of the pivot. Both kids exert a downward force on the seesaw due to their weights. Girl’s weight is trying to turn the seesaw anticlockwise whilst Boys's weight is trying to turn the seesaw clockwise. 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.
Thus 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.
2. Moments Acting On A Beam Balance:
When slightly different weights are placed on the two pans of a beam balance, the beam comes to rest at an angle with the horizontal. The beam is supported at a fixed single point by a pivot. The net torque about this fixed single point due to the two weights which are not zero, at the equilibrium position. The whole system does not continue to rotate about the fixed point because the moment is balanced.
3. Load In A Wheelbarrow:
Generally, the principle of moments is used in the lever system where the heavy loads are to be lifted.
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. Hence, by using the principle of moments heavy load can be lifted or replaced by the lower amount of efforts.
Q.11: Write three necessary conditions for two forces to form a couple.
Ans: Necessary Conditions For Two Forces To Form A Couple:
To form a couple, two forces must be:
- Equal in magnitude
- Parallel, but opposite in direction
- Separated by a distanced
Q.12: If two forces 5 N each form a couple and the moment arm is 0.5 m .Then what will be torque of the couple?
Solution:
Data:
- F = 5 N
- d = 0.5 cm
- τ = ?
Formula:
τ = F x d
Calculation:
τ = 50 x 0.5 = 2.5 Nm
Ans: Thus, The torque of the couple will be 2.5 Nm.Q.13: List three states of equilibrium.
Ans: STATES OF EQUILIBRIUM:
There are three states of equilibrium:
- Stable equilibrium
- Unstable equilibrium and
- Neutral 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
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.14: Why a body in unstable equilibrium does not return back to it original position when given a small tilt?
Ans: The center of gravity of the body is at its highest position in a state of unstable equilibrium. As the body topples over about its base (tip), its center of gravity moves towards its lower position and does not return back to its previous or original position.
Q.15: Why racing cars are made heavy at bottom?
Ans: The sports cars are made heavy at bottom which increases the base area of the car and lowers the center of mass and hence increases the stability.
Q.16: Why the base area of Bunsen burner is made large?
Ans: The base area of Bunsen burner is made large because having a large base ensures that the vertical line through the center of gravity of the object will lie within the base of the object when it is tilted. While having a heavy base ensures that the center of gravity is low. therefore the Bunsen burner will be very stable.
This is also reduce the chances of the burner accidentally tipping over, knocking over a lit Bunsen burner could have very bad result.
TEXT BOOK EXERCISE
For Numericals Click HereSection (B) Structured Questions
Forces on bodies
1. a) Define like and unlike forces.
Ans: See above in Self Assessment Questions - Q.1.
1. b) A pair of like parallel forces 15 N each are acting on a body. Find their resultant.
Ans: For Solution of Numericals Click Here
1. c) Two unlike parallel forces 10 N each acting along same line. Find their resultant.
Ans: For Solution of Numericals Click Here
Addition of forces
2. a) Describe the head to tail rule of vector addition of forces.
Ans: See above in Self Assessment Questions - Q.4.
b) Three forces 12 N along x-axis, 8 N making an angle of 45° with x-axis and 8 N along y-axis.
i) Find their resultant
ii) Find the direction of resultant
Ans: For Solution of Numericals Click Here
Resolution of forces
3. a) How a force can be 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.
- Horizontal component OB
- Vertical component BA
(i) Horizontal component OB:
The components OB which is along x-axis is called horizontal component of force and denoted by Fx.
(ii) Vertical component BA:
The components BA which is along y-axis is called vertical component of force and denoted by Fy.
The components OB = Fx and BA = Fy are perpendicular to each other. They are called the perpendicular components of OA = F.
Therefore,
F = Fx + Fy .................(i)
Magnitude Of Component Fx and Fy:
The trigonometric ratios can be used to find the magnitudes Fx and Fy. In right angled triangle ΔOBA.
Equations (ii) and (iii) give the perpendicular components respectively.
3. b) A gardener is driving a lawnmower with a force o of 80 N that makes an angle of 40 with the ground. i) Find its horizontal component
ii) Find its vertical component
Ans: For Solution of Numericals Click Here
4. a) How can you determine a force from its rectangular components?
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 Fx and Fy 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 Fx and Fy respectively.Thus,
F = Fx + Fy
Magnitude Of A Force (Vector):
Consider right angle triangle OPR
- Fx = OP = Base
- Fy = 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 = Fx2 + Fy2
Therefore,
Direction Of Force (Vector):
The direction of F with x-axis is given by
4. b) Horizontal and vertical components of a force are 4 N and 3 N respectively. Find
i) Resultant force
ii) Direction of resultant
Ans: For Solution of Numericals Click Here
Moment of force
5. a) What do you mean by moment of force?
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).
5. b) A spanner of 0.3 m length can produce a torque of 300 Nm.
i) determine the force applied on it.
ii) What should be the length of the spanner if torque is to be increased to 500 Nm with same applied force.
Ans: For Solution of Numericals Click Here
Principle of moments
6. a) State the principle of 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."
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."
b) A uniform meter rule is supported at its center is balanced by two forces 12 N and 20 N
i) if 20 N force is placed at a distance of 3 m from pivot find the position of 12 N force on the other side of pivot
ii) if the 20N force is moved to 4cm from pivot then find force to replace 12N force.
Ans: For Solution of Numericals Click Here
Center of mass
7. a) Define Center of mass or Center of gravity.
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."
6. b) How will you determine the Center of mass or Center of gravity?
Ans: Center of mass or Center of gravity of different object can be determine as:
(a) 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.
(b) 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.
Couple
8. a) Define couple as a pair of forces tending to produce torque?
Ans: COUPLE:
Couple is define as:
"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.
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.
8. b) A mechanic uses a double arm spanner to turn a nut. He applies a force of 15 N at each end of the spanner and produces a torque of 60 Nm. What is the length of the moment arm of the couple?
Ans: For Solution of Numericals Click Here
8. c) If he wants to produce a torque of 80 Nm with same spanner then how much force he should apply?
Ans: For Solution of Numericals Click Here
Equilibrium
9. a) state two conditions necessary for an object to be in equilibrium.
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 , ………., Fn are acting on a body then according to first condition of equilibrium:
F1 + F2 + F3 + ……… + Fn = 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 + F2x + F3x + ……… + Fnx = 0 and
F1y + F2y + F3y + ………. + Fny = 0 or
ΣFx = 0 ............. (ii)
ΣFy = 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
9. b) A uniform metre rule is balanced at the 30 cm mark when a load of 0.80 N is hung at the zero mark.
i) At what point on the rule is the Centre of gravity of the rule?
ii) calculate the weight of the rule
Ans: For Solution of Numericals Click Here
