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Chapter 3: Problem 36

You push your book across the desk, and it slides off the edge and falls to the floor. Identify the forces that act on the book during the three parts of this scenario: (a) while you are pushing the book, (b) while the book is sliding, and (c) while the book is falling.

Short Answer

Expert verified
During pushing: applied force, frictional force, gravitational force, and normal force. During sliding: frictional force, gravitational force, and normal force. During falling: gravitational force and air resistance.

Step by step solution

01

- Identify Forces while Pushing

While you are pushing the book across the desk, there are several forces acting on it: (1) Applied force: This is the force exerted by you to move the book. (2) Frictional force: Opposes the motion of the book and acts in the direction opposite to the applied force. (3) Gravitational force: Acts downward due to the Earth's gravity. (4) Normal force: Perpendicular to the surface of the desk, balancing the gravitational force.
02

- Identify Forces while Sliding

As the book slides across the desk, the applied force is no longer acting. The forces that remain are: (1) Frictional force: Still acting opposite to the direction of motion, but likely reduced as the book slows down. (2) Gravitational force: Constantly acting downward. (3) Normal force: Continuing to act perpendicular to the desk's surface, opposing gravity.
03

- Identify Forces while Falling

When the book slides off and begins to fall, the forces change again: (1) Gravitational force: Continues to act downward, now causing the book to accelerate towards the floor. (2) Air resistance: Acts upward, opposing the motion of the falling book. The normal and frictional forces are no longer present once the book is in free fall.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Applied Force
When you push the book across the desk, you are exerting an **applied force**. This is a force that comes from an external source, like a person or an object pushing or pulling. In this case, your hand is providing the applied force, moving the book in the direction you are pushing.
Applied forces can cause objects to start moving, stop moving, or change direction. This force is essential to overcome static friction and get an object like a book to start sliding.
Frictional Force
Frictional force always acts in the direction opposite to the applied force. While you're pushing the book, friction between the book and the desk resists this motion.
There are two main types of friction to consider:
  • Static friction: Prevents the book from moving when it is at rest.
  • Kinetic friction: Acts on the book once it starts sliding.
As the book moves, kinetic friction helps slow it down gradually. In some cases, if the friction is strong enough, it can even stop the book before it reaches the edge of the desk.
Gravitational Force
Gravitational force is the force exerted by the Earth that pulls objects towards its center. This force acts downward on the book at all times, whether it is being pushed, sliding, or falling.
The magnitude of the gravitational force can be calculated using the equation: ewline F_g = mg ewline where: ewline m = mass of the book ewline g = acceleration due to gravity (approximately 9.8 m/s²)
Understanding gravitational force is crucial in predicting how objects will move when dropped or thrown. It's why the book accelerates toward the floor once it slides off the desk.
Normal Force
Normal force is always perpendicular to the surface that an object is in contact with. When the book is on the desk, the desk exerts an upward normal force to balance the downward gravitational force.
You can think of normal force as a support force that prevents objects from simply falling through surfaces. The magnitude of the normal force can be equal to the gravitational force if there's no vertical acceleration.
Air Resistance
Air resistance, or drag, is the force exerted by air against the motion of an object. When the book slides off the desk and starts falling, it encounters air resistance, which acts upward and opposes the downward motion caused by gravity.
The effect of air resistance depends on factors such as the object's speed, surface area, and shape. Generally, for small and dense objects like books, the air resistance is relatively minor compared to the gravitational force.
Free Fall
Free fall describes the motion of an object when it is falling solely under the influence of gravity, with no other forces acting on it except air resistance. When the book falls off the desk, it is briefly in a state of free fall.
During free fall, the only significant force is the gravitational force. This causes the book to accelerate downward at a rate of approximately 9.8 m/s², assuming negligible air resistance. Understanding free fall helps in analyzing motion and predicting how long it will take objects to reach the ground.

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