Problem 22 - University Physics with Modern Physics

Question

Imagine that you are holding a book weighing 4 \(\mathrm{N}\) at rest on the palm of your hand. Complete the following sentences: (a) A downward force of magnitude 4 \(\mathrm{N}\) is exerted on the book by _____. (b) An upward force of magnitude _____ is exerted on _____ by your hand. (c) Is the upward force in part \((b)\) the reaction to the downward force in part \((a) ?\) (d) The reaction to the force in part (a) is a force of magnitude _____, exerted on _____ by _____. Its direction is _____. (e) The reaction to the force in part (b) is a force of magnitude _____, exerted on _____ by _____. Its direction is _____. (f) The forces in parts (a) and (b) are equal and opposite because of Newton's _____ law. (g) The forces in parts \((b)\) and (e) are equal and opposite because of Newton's _____ law. Now suppose that you exert an upward force of magnitude 5 \(\mathrm{N}\) on the book. (h) Does the book remain im equilibrium? (i) Is the force exerted on the book by your hand equal and opposite to the force exerted on the book by the earth? (i) Is the force exerted on the book by the earth equal and opposite to the force exerted on the earth by the book? (k) Is the force exerted on the book by your hand equal and opposite to the force exerted on your hand by the book? Finally, suppose you snatch your hand away while the book is moving upward. (I) How many forces then act on the book? (m) Is the book in equilibrium?

Step-by-Step Solution

Answer

(a) Earth (b) 4 N, the book (c) No (d) 4 N, Earth, upward (e) 4 N, your hand, downward (f) Second (g) Third (h) No (i) No (j) Yes (k) Yes (l) One (m) No

Step 1: Identifying the Force in Part (a)

To determine the downward force exerted on the book, consider the force of gravity acting on the book. This force is always exerted by Earth on objects within its gravitational field. (a) A downward force of magnitude 4 \(\mathrm{N}\) is exerted on the book by Earth.

Step 2: Calculating the Upward Force in Part (b)

When the book is at rest on your hand, the upward force is the normal force exerted by the hand, which is equal in magnitude and opposite in direction to the gravitational force.(b) An upward force of magnitude 4 \(\mathrm{N}\) is exerted on the book by your hand.

Step 3: Identifying if Forces in (a) and (b) are Reaction Pair

Newton's Third Law defines action-reaction pairs as equal in magnitude and opposite in direction, but acting on different objects. The forces described in part (b) on the book and part (a) on the book itself are not action-reaction pairs. (c) No, the upward force in part (b) is not the reaction to the downward force in part (a).

Step 4: Identifying the Reaction to Force in Part (a)

According to Newton's Third Law, every action has an equal and opposite reaction. The reaction to the gravitational force in part (a) would be the book exerting a force on Earth.(d) The reaction to the force in part (a) is a force of magnitude 4 \(\mathrm{N}\), exerted on Earth by the book. Its direction is upwards.

Step 5: Identifying the Reaction to the Force in Part (b)

The reaction to the force exerted by your hand on the book in part (b) is the force exerted by the book on your hand.(e) The reaction to the force in part (b) is a force of magnitude 4 \(\mathrm{N}\), exerted on your hand by the book. Its direction is downwards.

Step 6: Explaining Part (f) Using Newton's Laws

The forces described in parts (a) and (b) bring the book to equilibrium because they cancel each other out. (f) The forces in parts (a) and (b) are equal and opposite because of Newton's Second Law.

Step 7: Explaining Part (g) Using Newton's Laws

The forces on the book by the hand and on the hand by the book are action-reaction pairs as described by Newton's laws. (g) The forces in parts (b) and (e) are equal and opposite because of Newton's Third Law.

Step 8: Analyzing the Change in Forces When Exerting 5 N

If you exert an upward force greater than the weight of the book (5 \(\mathrm{N}\) vs. 4 \(\mathrm{N}\)), the book experiences a net upward force.(h) No, the book does not remain in equilibrium.

Step 9: Equivalence of Forces in Part (i)

The forces exerted on the book by the hand and by Earth are not equal when exerting 5 \(\mathrm{N}\).(i) No, these forces are not equal and opposite.

Step 10: Analyzing Force on Earth by Book in Part (j)

When considering Newton's Third Law, the force that the earth experiences due to the book is equal and opposite to the force on the book by Earth. (j) Yes, the force exerted on the book by the Earth is equal and opposite to the force exerted on the Earth by the book.

Step 11: Analyzing Force on Hand by Book in Part (k)

The force on your hand is equal and opposite to the force exerted by your hand due to Newton’s Third Law. (k) Yes, the force exerted on the book by your hand is equal and opposite to the force exerted on your hand by the book.

Step 12: Identifying Forces When Hand Is Removed in Part (l)

When your hand is removed, the only force acting would be gravitational force. (l) One force acts on the book.

Step 13: Determining Equilibrium Status in Part (m)

Without an upward force to balance gravity, the book will not be in equilibrium. (m) No, the book is not in equilibrium.

Key Concepts

Force Equilibrium

Understanding force equilibrium is crucial to grasp many physics concepts. Equilibrium occurs when all forces acting on an object balance each other out, causing it to either remain at rest or move at a constant velocity. In our exercise, the book resting on your palm is in equilibrium. The forces include:

* The downward gravitational force (4 N), which the Earth exerts on the book.
* The upward force exerted by your hand (also 4 N), which is the normal force.

When these forces are equal in magnitude and opposite in direction, the net force is zero, fulfilling the condition for equilibrium. This balance ensures that the book remains stationary in your hand. If an imbalance occurs, such as exerting a 5 N upward force, the book would accelerate upwards as equilibrium breaks. Therefore, understanding equilibrium helps predict and explain the behavior of objects under various forces.

Action-Reaction Pairs

Newton's Third Law introduces the concept of action-reaction pairs. It tells us that for every action force, there is an equal and opposite reaction force. However, it's essential to note that these forces act on different objects, never the same. Let's explore our exercise further:

* The action is the Earth pulling the book down with a 4 N gravitational force.
* The reaction is the book pulling the Earth up with a 4 N force, although imperceptible due to Earth's massive size.

This pair acts on two separate entities: the book and Earth. Similarly, when your hand exerts a force on the book, the book responds with an equal force back on your hand, forming another pair:

* Your hand pushes up on the book (4 N).
* The book pushes down on your hand with (4 N).

Understanding these pairs helps clarify that action and reaction don't cancel each other out since they affect different objects.

Gravitational Force

Gravitational force is a fundamental force that pulls objects toward each other. On Earth, this force gives weight to the objects. The weight of an object, like the book in our exercise, is the gravitational force exerted by Earth and is calculated as the product of its mass and the acceleration due to gravity (9.81 m/s²).

* For the book weighing 4 N, Earth continuously pulls it downward.
* This gravitational pull is experienced by all masses within Earth's gravitational field.

In this scenario, the book's weight directly results from the gravitational force. When you increase the upward force to 5 N, you're temporarily overcoming the gravitational pull, moving the book upwards. If your hand is removed while the book is airborne, only gravity will act on it, pulling it back down.

Gravitational force is a key player in maintaining the natural motion and position of objects, and it is crucial for understanding concepts such as weight and free-fall.