Introduction to Newton’s Second Law of Motion with Example Problem

Summary

This video explains Newton's Second Law of Motion through an interactive, step-by-step example. It covers the key formula: net force equals mass times acceleration, and introduces concepts like vectors, force diagrams, and the importance of free body diagrams. The script walks through a problem involving a book, using forces like gravity, friction, and applied force to calculate acceleration and forces in both the X and Y directions. The video emphasizes the practical use of Newton's Second Law, helping viewers understand both the calculations and the underlying physics concepts.

Takeaways

• 😀 Newton's Second Law of Motion is defined as F = ma, where force (F) equals mass (m) times acceleration (a). Both force and acceleration are vectors.
• 😀 The uppercase Greek letter sigma (Σ) is used to represent summation, indicating the sum of all forces acting on an object.
• 😀 The first step in solving problems involving Newton's Second Law is to identify and list all forces acting on the object.
• 😀 A free body diagram is crucial for understanding the directions and magnitudes of the forces acting on an object.
• 😀 In the Y direction, the forces acting on the book include the force of gravity (down) and the normal force (up).
• 😀 The net force in the Y direction is zero if there is no vertical movement, meaning the force normal equals the force of gravity.
• 😀 The acceleration in the Y direction of the book is zero since there is no vertical movement when a horizontal force is applied.
• 😀 Newton's Second Law is applied again to find the acceleration in the X direction, using the net force in that direction.
• 😀 To find acceleration in the X direction, we subtract the force of friction from the applied force and divide by the object's mass.
• 😀 The acceleration of the book is 0.86 meters per second squared, calculated using the formula a = (F applied - F friction) / mass.
• 😀 When forces are constant, the acceleration is constant, allowing the use of uniformly accelerated motion equations to solve for displacement or time in future problems.

Q & A

What is Newton's Second Law of Motion?

Newton's Second Law of Motion states that the sum of all forces acting on an object (net force) equals the object's mass multiplied by its acceleration (F = ma), where both force and acceleration are vectors.

What does the Greek letter sigma (Σ) represent in Newton's Second Law?

The Greek letter sigma (Σ) represents summation. In the context of Newton's Second Law, ΣF means the sum of all forces acting on an object.

How do you convert the mass of the book from grams to kilograms?

To convert the mass from grams to kilograms, divide the mass by 1000. For example, 1627 grams is equal to 1.627 kilograms.

Why do we need to convert the mass to kilograms when calculating force?

We need to convert the mass to kilograms because the unit for force (newton) is defined as 1 kilogram meter per second squared. Without the correct unit for mass, the calculation of force wouldn't be correct.

What are the forces acting on the book in the free body diagram?

The forces acting on the book are: the force of gravity (downward), the normal force (upward, perpendicular to the surface), the applied force (to the right), and the force of friction (to the left).

How do you calculate the magnitude of the force of gravity?

The magnitude of the force of gravity is calculated by multiplying the mass of the object (in kilograms) by the acceleration due to gravity (9.81 m/s²). For the book, it is 1.627 kg × 9.81 m/s² = 16 newtons.

What is the acceleration in the Y direction for the book?

The acceleration in the Y direction is zero because the book doesn't move up or down; it only moves horizontally. Therefore, the forces in the Y direction (gravity and normal force) cancel each other out.

How do we find the net force in the X direction?

To find the net force in the X direction, subtract the force of friction (to the left) from the applied force (to the right). This gives us the net force in the X direction, which is then used to calculate acceleration.

What formula is used to calculate acceleration in the X direction?

The formula used to calculate acceleration in the X direction is: a = (F_applied - F_friction) / mass. In the given problem, a = (5.0 N - 3.6 N) / 1.627 kg, which results in an acceleration of 0.86 m/s².

Why does the acceleration of the book equal zero in the Y direction?

The acceleration of the book in the Y direction is zero because there is no movement vertically. The forces of gravity and the normal force balance out, resulting in no vertical acceleration.

How does the concept of constant forces relate to the book's motion?

Since all the forces acting on the book are constant (the applied force, friction, and gravity), the net force is constant, which results in constant acceleration. This means we can use uniformly accelerated motion (UAM) equations to solve for displacement or time, given the acceleration.