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

Hey there, future physics ace! Let's get you prepped and confident for the AP Physics C: Mechanics exam. We're diving into Newton's Second Law, a cornerstone of mechanics. Think of it as the 'why' behind all the motion you see. Let's break it down and make it stick!

#Newton's Second Law: The Heart of Motion

Newton's Second Law is all about how forces cause changes in motion. It's your go-to for understanding why things speed up, slow down, or change direction. It’s the bridge between force and motion.

#The Formula

The law is mathematically expressed as:

$$\vec{a}_{sys} = \frac{\sum \vec{F}}{m_{sys}} = \frac{\vec{F}_{net}}{m_{sys}}$$

Where:

• $\vec{a}_{sys}$ is the acceleration of the system's center of mass.
• $\sum \vec{F}$ or $\vec{F}_{net}$ is the net force acting on the system.
• $m_{sys}$ is the total mass of the system.

#Conditions for Velocity Changes

Let's dig into the nitty-gritty of what makes things speed up, slow down, or change direction. It's all about forces!

#Unbalanced Forces 🚫

• Definition: When the net force acting on a system is NOT zero. Forces don't cancel each other out.
• Effect: Causes the system to accelerate in the direction of the net force. If there's a net force, there's acceleration!
• Source: Can be a single force or multiple forces that don't balance.

#Newton's Second Law (Again!)

• Connection: Links the acceleration of a system's center of mass to the net force. It's the formula in action.
• Proportionality: Acceleration is directly proportional to the net force (more force = more acceleration) and inversely proportional to the system's mass (more mass = less acceleration). 🏋️
• Math: Remember that formula? $$\vec{a}_{sys} = \frac{\sum \vec{F}}{m_{sys}}$$. It tells you everything!

#Net External Force

• Definition: The sum of all forces acting on a system from outside the system.
• Impact: Determines if the velocity of the system's center of mass will change. No net force, no change in velocity.
• Acceleration: A non-zero net external force is required for acceleration. If the net external force is zero, the system's center of mass will maintain a constant velocity (or remain at rest). 🏁
• Internal Forces: Internal forces within the system do not affect the motion of the center of mass. Think of it like pushing on the dashboard of your car – it won’t make the car move.

#

Practice Question

#Multiple Choice Questions

1. A 2 kg object is subjected to a net force of 10 N. What is the magnitude of the object's acceleration? (A) 2 m/s² (B) 5 m/s² (C) 10 m/s² (D) 20 m/s²

2. If the net force acting on an object is doubled, what happens to the object's acceleration? (A) It is halved. (B) It remains the same. (C) It is doubled. (D) It is quadrupled.

3. A 5 kg box is at rest on a frictionless surface. If a 20 N force is applied horizontally to the box, what is the box's acceleration? (A) 0 m/s² (B) 2 m/s² (C) 4 m/s² (D) 100 m/s²

#Free Response Question

A 3 kg block is initially at rest on a horizontal, frictionless surface. A horizontal force of 12 N is applied to the block.

(a) Calculate the acceleration of the block. (2 points)

(b) If the force is applied for 5 seconds, calculate the final velocity of the block. (2 points)

(c) After 5 seconds, the force is removed. What is the block's velocity after 10 seconds? (2 points)

(d) Now, consider a scenario where the same 3 kg block is on a surface with friction. The coefficient of kinetic friction between the block and the surface is 0.2. If the same 12 N force is applied, calculate the new acceleration of the block. (4 points)

#FRQ Scoring Breakdown

(a) Acceleration Calculation (2 points)

• 1 point for using Newton's Second Law: $a = F/m$
• 1 point for correctly substituting and calculating: $a = 12 N / 3 kg = 4 m/s^2$

(b) Final Velocity Calculation (2 points)

• 1 point for using the kinematic equation: $v = v_0 + at$
• 1 point for correct substitution and calculation: $v = 0 + (4 m/s^2)(5 s) = 20 m/s$

(c) Velocity after force removal (2 points)

• 1 point for recognizing that no force means no acceleration
• 1 point for stating that the velocity remains constant: $v = 20 m/s$

(d) Acceleration with Friction (4 points)

• 1 point for calculating the frictional force: $f = \mu * N = 0.2 * (3 kg * 9.8 m/s^2) = 5.88 N$
• 1 point for finding the net force: $F_{net} = 12 N - 5.88 N = 6.12 N$
• 1 point for using Newton's Second Law: $a = F_{net} / m$
• 1 point for correct calculation: $a = 6.12 N / 3 kg = 2.04 m/s^2$

#Final Exam Focus

Okay, you're almost there! Here’s what to focus on for the exam:

• Newton's Second Law: Know it inside and out. Be ready to apply it in various scenarios. It's a core concept.
• Free-Body Diagrams: Master drawing them. They are key to solving force-related problems. Always start with a good diagram.
• Net Force: Understand how to calculate the net force by considering all forces acting on a system.
• Connections: Be ready for questions that combine Newton's Second Law with kinematics and other concepts.
• Problem Solving: Practice, practice, practice. The more problems you solve, the more comfortable you'll be.

You are ready to ace this exam! Good luck, and remember, physics is awesome! 🚀