Page 1
The Forces
Contents
1 Introduction to Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Example 2 (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Example 2 (From Book, Modi?ed) . . . . . . . . . . . . . . . . . . 4
3 Electromagnetic (EM) Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.2 Example 4.1 (From Book) . . . . . . . . . . . . . . . . . . . . . . . 5
4 Nuclear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Weak Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Scope of Classical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 Worked Out Examples from Book . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 Short Answer Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Page 2
The Forces
Contents
1 Introduction to Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Example 2 (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Example 2 (From Book, Modi?ed) . . . . . . . . . . . . . . . . . . 4
3 Electromagnetic (EM) Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.2 Example 4.1 (From Book) . . . . . . . . . . . . . . . . . . . . . . . 5
4 Nuclear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Weak Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Scope of Classical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 Worked Out Examples from Book . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 Short Answer Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Introduction to Forces
A force is a push or pull that can alter an object’s state of rest or motion. Pushing a
table exerts a force away from you, while pulling a rope exerts a force toward you.
Holding a heavy object requires more force than a light one. Nonliving objects also
exertforces: windpushesyouinastorm,waterliftsacork,andacombattractspaper
pieces after combing dry hair.
Force is an interaction between two objects. For any force, we ask: (1) Which object
exerts it? (2) On which object is it exerted? For example, a table exerts an upward
force on a block placed on it, and the block exerts a downward force on the table.
The SI unit of force is the newton (N), approximately the force needed to hold a 102
g mass near Earth’s surface. A precise de?nition will be given in the next chapter
using Newton’s laws.
Force is a vector quantity, with magnitude and direction. Multiple forces combine
using vector addition.
Newton’s Third Law states: If object A exerts a force
?
F on object B, then B exerts
a force -
?
F on A, along the line joining them. These form an action-reaction pair.
Examples include:
• Aropeexertsanupwardforceonahangingblock;theblockexertsadownward
force on the rope.
• A block on a table is supported by an upward force; the block presses down-
ward on the table.
Forces are classi?ed into four types:
• Gravitational: Attraction between masses.
• Electromagnetic: Forces between charged or magnetic objects.
• Nuclear: Forces within atomic nuclei.
• Weak: Forces in particle transformations.
1.1 Solved Examples
1.1.1 Example 1
A student pulls a cart with a force of 15 N eastward. Describe the action-reaction
pair.
Solution:
• Action: The student exerts a 15 N force eastward on the cart.
• Reaction: The cart exerts a 15 N force westward on the student.
These forces are equal in magnitude, opposite in direction, and act along the line of
contact.
Page 3
The Forces
Contents
1 Introduction to Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Example 2 (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Example 2 (From Book, Modi?ed) . . . . . . . . . . . . . . . . . . 4
3 Electromagnetic (EM) Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.2 Example 4.1 (From Book) . . . . . . . . . . . . . . . . . . . . . . . 5
4 Nuclear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Weak Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Scope of Classical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 Worked Out Examples from Book . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 Short Answer Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Introduction to Forces
A force is a push or pull that can alter an object’s state of rest or motion. Pushing a
table exerts a force away from you, while pulling a rope exerts a force toward you.
Holding a heavy object requires more force than a light one. Nonliving objects also
exertforces: windpushesyouinastorm,waterliftsacork,andacombattractspaper
pieces after combing dry hair.
Force is an interaction between two objects. For any force, we ask: (1) Which object
exerts it? (2) On which object is it exerted? For example, a table exerts an upward
force on a block placed on it, and the block exerts a downward force on the table.
The SI unit of force is the newton (N), approximately the force needed to hold a 102
g mass near Earth’s surface. A precise de?nition will be given in the next chapter
using Newton’s laws.
Force is a vector quantity, with magnitude and direction. Multiple forces combine
using vector addition.
Newton’s Third Law states: If object A exerts a force
?
F on object B, then B exerts
a force -
?
F on A, along the line joining them. These form an action-reaction pair.
Examples include:
• Aropeexertsanupwardforceonahangingblock;theblockexertsadownward
force on the rope.
• A block on a table is supported by an upward force; the block presses down-
ward on the table.
Forces are classi?ed into four types:
• Gravitational: Attraction between masses.
• Electromagnetic: Forces between charged or magnetic objects.
• Nuclear: Forces within atomic nuclei.
• Weak: Forces in particle transformations.
1.1 Solved Examples
1.1.1 Example 1
A student pulls a cart with a force of 15 N eastward. Describe the action-reaction
pair.
Solution:
• Action: The student exerts a 15 N force eastward on the cart.
• Reaction: The cart exerts a 15 N force westward on the student.
These forces are equal in magnitude, opposite in direction, and act along the line of
contact.
1.1.2 Example 2 (Conceptual)
A book rests on a table. Identify the forces on the book and their action-reaction
pairs.
Solution:
• Normal force: The table exerts an upward force F on the book; the book exerts a
downward force F on the table.
• Gravitationalforce: TheEarthexertsadownwardforce mg onthebook; thebook
exerts an upward force mg on the Earth.
2 Gravitational Force
Any two masses attract each other with a gravitational force. For two point masses
m
1
and m
2
separated by distance r, the force is:
F = G
m
1
m
2
r
2
Page 4
The Forces
Contents
1 Introduction to Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Example 2 (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Example 2 (From Book, Modi?ed) . . . . . . . . . . . . . . . . . . 4
3 Electromagnetic (EM) Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.2 Example 4.1 (From Book) . . . . . . . . . . . . . . . . . . . . . . . 5
4 Nuclear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Weak Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Scope of Classical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 Worked Out Examples from Book . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 Short Answer Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Introduction to Forces
A force is a push or pull that can alter an object’s state of rest or motion. Pushing a
table exerts a force away from you, while pulling a rope exerts a force toward you.
Holding a heavy object requires more force than a light one. Nonliving objects also
exertforces: windpushesyouinastorm,waterliftsacork,andacombattractspaper
pieces after combing dry hair.
Force is an interaction between two objects. For any force, we ask: (1) Which object
exerts it? (2) On which object is it exerted? For example, a table exerts an upward
force on a block placed on it, and the block exerts a downward force on the table.
The SI unit of force is the newton (N), approximately the force needed to hold a 102
g mass near Earth’s surface. A precise de?nition will be given in the next chapter
using Newton’s laws.
Force is a vector quantity, with magnitude and direction. Multiple forces combine
using vector addition.
Newton’s Third Law states: If object A exerts a force
?
F on object B, then B exerts
a force -
?
F on A, along the line joining them. These form an action-reaction pair.
Examples include:
• Aropeexertsanupwardforceonahangingblock;theblockexertsadownward
force on the rope.
• A block on a table is supported by an upward force; the block presses down-
ward on the table.
Forces are classi?ed into four types:
• Gravitational: Attraction between masses.
• Electromagnetic: Forces between charged or magnetic objects.
• Nuclear: Forces within atomic nuclei.
• Weak: Forces in particle transformations.
1.1 Solved Examples
1.1.1 Example 1
A student pulls a cart with a force of 15 N eastward. Describe the action-reaction
pair.
Solution:
• Action: The student exerts a 15 N force eastward on the cart.
• Reaction: The cart exerts a 15 N force westward on the student.
These forces are equal in magnitude, opposite in direction, and act along the line of
contact.
1.1.2 Example 2 (Conceptual)
A book rests on a table. Identify the forces on the book and their action-reaction
pairs.
Solution:
• Normal force: The table exerts an upward force F on the book; the book exerts a
downward force F on the table.
• Gravitationalforce: TheEarthexertsadownwardforce mg onthebook; thebook
exerts an upward force mg on the Earth.
2 Gravitational Force
Any two masses attract each other with a gravitational force. For two point masses
m
1
and m
2
separated by distance r, the force is:
F = G
m
1
m
2
r
2
Page 5
The Forces
Contents
1 Introduction to Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Example 2 (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Example 2 (From Book, Modi?ed) . . . . . . . . . . . . . . . . . . 4
3 Electromagnetic (EM) Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1.2 Example 4.1 (From Book) . . . . . . . . . . . . . . . . . . . . . . . 5
4 Nuclear Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 5
5 Weak Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Scope of Classical Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1 Solved Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6.1.1 Example (Conceptual) . . . . . . . . . . . . . . . . . . . . . . . . . 6
7 Worked Out Examples from Book . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.3 Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
8 Short Answer Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1 Introduction to Forces
A force is a push or pull that can alter an object’s state of rest or motion. Pushing a
table exerts a force away from you, while pulling a rope exerts a force toward you.
Holding a heavy object requires more force than a light one. Nonliving objects also
exertforces: windpushesyouinastorm,waterliftsacork,andacombattractspaper
pieces after combing dry hair.
Force is an interaction between two objects. For any force, we ask: (1) Which object
exerts it? (2) On which object is it exerted? For example, a table exerts an upward
force on a block placed on it, and the block exerts a downward force on the table.
The SI unit of force is the newton (N), approximately the force needed to hold a 102
g mass near Earth’s surface. A precise de?nition will be given in the next chapter
using Newton’s laws.
Force is a vector quantity, with magnitude and direction. Multiple forces combine
using vector addition.
Newton’s Third Law states: If object A exerts a force
?
F on object B, then B exerts
a force -
?
F on A, along the line joining them. These form an action-reaction pair.
Examples include:
• Aropeexertsanupwardforceonahangingblock;theblockexertsadownward
force on the rope.
• A block on a table is supported by an upward force; the block presses down-
ward on the table.
Forces are classi?ed into four types:
• Gravitational: Attraction between masses.
• Electromagnetic: Forces between charged or magnetic objects.
• Nuclear: Forces within atomic nuclei.
• Weak: Forces in particle transformations.
1.1 Solved Examples
1.1.1 Example 1
A student pulls a cart with a force of 15 N eastward. Describe the action-reaction
pair.
Solution:
• Action: The student exerts a 15 N force eastward on the cart.
• Reaction: The cart exerts a 15 N force westward on the student.
These forces are equal in magnitude, opposite in direction, and act along the line of
contact.
1.1.2 Example 2 (Conceptual)
A book rests on a table. Identify the forces on the book and their action-reaction
pairs.
Solution:
• Normal force: The table exerts an upward force F on the book; the book exerts a
downward force F on the table.
• Gravitationalforce: TheEarthexertsadownwardforce mg onthebook; thebook
exerts an upward force mg on the Earth.
2 Gravitational Force
Any two masses attract each other with a gravitational force. For two point masses
m
1
and m
2
separated by distance r, the force is:
F = G
m
1
m
2
r
2
2.1.2 Example 2 (From Book, Modi?ed)
Calculate the gravitational force on a 5 kg object near Earth’s surface (g = 10m/s
2
).
Solution:
F = mg = 5×10 = 50N, downward
3 Electromagnetic (EM) Force
Charged particles exert electromagnetic forces. For two charges q
1
and q
2
at rest,
separated by distance r, the Coulomb force is:
F =
1
4pe
0
q
1
q
2
r
2
where e
0
= 8.854×10
-12
C
2
/N·m
2
, and
1
4pe
0
˜ 9×10
9
N·m
2
/C
2
. The force is
repulsive for like charges, attractive for unlike charges.
Electromagnetic forces bind electrons (-1.6×10
-19
C) to protons (+1.6×10
-19
C) in
atoms and form molecules. They cause a comb to attract paper pieces after combing
hair.
When surfaces touch, atoms interact via electromagnetic forces, producing contact
forces:
• Normal force: Perpendicular to the surface, typically repulsive (e.g., a table sup-
ports a book).
• Friction: Parallel to the surface, resists motion (e.g., a rough tree trunk provides
friction).
Frictionless surfaces (e.g., smooth metal) exert only normal forces. Contact forces
obey Newton’s Third Law.
A stretched rope or string under tension exerts electromagnetic forces to pull objects
at its ends (e.g., in tug-of-war or supporting a block).
A spring exerts a force when stretched or compressed. For a spring with natural
length x
0
and current length x, the force is:
F = k|x-x
0
|
where k is the spring constant. The force pulls inward if stretched, pushes outward if
compressed.
Neutral macroscopic bodies have negligible electromagnetic forces unless charged or
in contact, unlike gravitational forces, which are always attractive.
3.1 Solved Examples
3.1.1 Example 1
Two charges, +3µC and-3µC, are 0.2 m apart. Find the force.
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