#AP Physics C: Mechanics - Newton's First Law Study Guide

Hey there, future physics pro! Let's break down Newton's First Law, also known as the law of inertia, and make sure you're totally prepped for the exam. This is all about understanding why things move (or don't move) the way they do. Let's dive in!

#1. Introduction to Newton's First Law

• Law of Inertia: Objects resist changes in their motion. If it's at rest, it stays at rest; if it's moving, it keeps moving at the same speed and in the same direction. 🪨

• Key Concepts: We'll explore vector force summation, translational equilibrium, and inertial reference frames to fully grasp this law. These concepts are all interconnected, and mastering them will give you a solid foundation for more complex topics.

Go to Vector Sum of Forces

Go to Translational Equilibrium

Go to Newton's First Law

Go to Balanced vs Unbalanced Forces

Go to Inertial Reference Frame

#2. Conditions for Constant Velocity

#Vector Sum of Forces

• Net Force: The total force acting on an object, calculated by adding individual forces as vectors. Remember, direction matters! 🏹

• Adding Forces: Forces in the same direction add up; forces in opposite directions subtract. Think of it like a tug-of-war. The net force is the 'winning' force.

• Vector Nature: We use vector addition to find the net force. This means we need to consider both the magnitude and direction of each force.

#Translational Equilibrium

• Definition: A state where the net force on an object is zero. This means the object is either at rest or moving at a constant velocity.

• Mathematical Representation: $$\sum \vec{F}_{i} = 0$$

  • $\sum$ means 'sum of'
  • $\vec{F}_{i}$ represents all individual forces acting on the system

• Constant Velocity: When the net force is zero, the object's velocity remains constant. This is a direct consequence of Newton's First Law.

#Newton's First Law (Law of Inertia)

• Core Principle: An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by an unbalanced force.

• No Net Force: If the net force on a system is zero ($\sum \vec{F}_{i} = 0$), the velocity remains constant. No force, no change in motion! 💡

• Inertia: The tendency of an object to resist changes in its state of motion. The more massive an object, the greater its inertia.

#Balanced vs. Unbalanced Forces

• Balanced Forces: Equal in magnitude but opposite in direction. They result in a net force of zero and no change in velocity. Think of a book resting on a table. ⚖️

• Unbalanced Forces: Result in a non-zero net force, causing a change in the object's velocity (acceleration). This is where things start to move or change their motion.

• Multi-Dimensional Forces: A system can have balanced forces in one direction (e.g., horizontal) but unbalanced forces in another (e.g., vertical). The velocity will only change in the direction of the unbalanced force. 🚗

  • Example: A car moving at a constant speed on a flat road has balanced horizontal forces (engine force and friction) but unbalanced vertical forces (gravity and normal force). The car is in equilibrium horizontally but not vertically. The vertical forces are balanced, meaning there is no acceleration in the vertical direction.

#Inertial Reference Frame

• Definition: A reference frame in which Newton's First Law holds true. An object with no net force acting on it will maintain a constant velocity.

• Non-Inertial Frames: Accelerating or rotating frames require 'fictitious forces' to explain motion. For example, the feeling of being pushed back in your seat when a car accelerates.

• Earth as an Inertial Frame: For most everyday situations, the Earth is considered an inertial reference frame. 🌍

• Exceptions: When dealing with extremely high speeds or strong gravitational fields, the Earth is no longer a perfect inertial frame.

#3. Final Exam Focus

Newton's First Law is a foundational concept that is essential for understanding all other topics in mechanics. Expect to see it in both multiple-choice and free-response questions, often combined with other concepts like forces, work, and energy.

• High-Priority Topics: Focus on understanding vector addition, free-body diagrams, and the conditions for translational equilibrium. These are the building blocks for solving more complex problems.

• Common Question Types: Expect questions that ask you to:

  • Identify forces acting on an object.
  • Determine if an object is in equilibrium.
  • Calculate the net force on an object.
  • Apply Newton's First Law to predict the motion of an object.

• Time Management: When tackling problems, start by drawing a free-body diagram. This will help you visualize the forces and avoid mistakes. Work methodically and don't rush.

• Common Pitfalls: Watch out for the common mistake of confusing equilibrium with 'no motion'. Remember, equilibrium means constant velocity, which can be zero.

• Strategies for Challenging Questions: Break down complex problems into smaller parts. Identify all the forces acting on the object and then apply Newton's First Law.

#4. Practice Questions

Practice Question

Multiple Choice Questions

1. A box is sliding down a ramp at a constant velocity. Which of the following statements is true about the forces acting on the box? (A) The net force is zero. (B) The gravitational force is the only force acting on the box. (C) The frictional force is greater than the gravitational force. (D) The normal force is equal to the gravitational force.

2. An object is moving in a straight line at a constant speed. Which of the following must be true? (A) There are no forces acting on the object. (B) The net force acting on the object is zero. (C) The object is accelerating. (D) The object is in a non-inertial reference frame.

3. A car is moving at a constant velocity on a flat road. Which of the following forces are balanced? (A) Only the engine force and friction. (B) Only the gravitational force and normal force. (C) Both the engine force and friction, and the gravitational force and normal force. (D) None of the above.

Free Response Question

A 2.0 kg block is pulled along a horizontal surface by a force of 10 N at an angle of 30° above the horizontal. The coefficient of kinetic friction between the block and the surface is 0.2. (a) Draw a free-body diagram of the block, labeling all forces.

(b) Calculate the normal force acting on the block.

(c) Calculate the frictional force acting on the block.

(d) Calculate the net force acting on the block.

(e) Calculate the acceleration of the block.

Answer Key

Multiple Choice

1. (A)
2. (B)
3. (C)

Free Response

(a) Free-body diagram: (1 point for each force correctly labeled) - Tension (T) at 30 degrees above horizontal - Weight (mg) downwards - Normal force (N) upwards - Friction (f) opposite to motion

(b) Normal force calculation (2 points): - Tension in the vertical direction: $T_y = 10 \sin(30) = 5 N$ - Weight of the block: $mg = 2 * 9.8 = 19.6 N$ - Normal force: $N = mg - T_y = 19.6 - 5 = 14.6 N$

(c) Frictional force calculation (2 points): - Frictional force: $f = \mu N = 0.2 * 14.6 = 2.92 N$

(d) Net force calculation (2 points): - Tension in the horizontal direction: $T_x = 10 \cos(30) = 8.66 N$ - Net force: $F_{net} = T_x - f = 8.66 - 2.92 = 5.74 N$

(e) Acceleration calculation (1 point): - Acceleration: $a = F_{net} / m = 5.74 / 2 = 2.87 m/s^2$

Good luck, you've got this! Remember to stay calm, read each question carefully, and apply the concepts we've covered. You're well-prepared to ace this exam! }