Introduction

Welcome to the FiveHive article for Unit 2.5 of AP Physics 1!

This subunit focuses on unbalanced net forces, with numerical calculations utilizing Newton’s Second Law of Motion. This will be the beginning of calculations using forces, which will continuously be used in future topics.

As usual, we will only cover the topics included in the CED for unit 2.5.

Newton’s Second Law

As learned in the previous subunit, translational equilibrium is when all the forces in a system are balanced, creating a net force of $0$, and there is no change in velocity for the objects within said system. 

However, forces are not always balanced, in which case they are measured in units of newtons, which is the same as $\frac{(kg)(m)}{s^2}$. Whenever a net force is applied to a system, it causes acceleration, leading to a change in velocity. 

To calculate force, Newton’s Second Law is used, most often simplified to one equation: $\vec{F}=ma$, though ${\vec{a}}_{sys}=\frac{\sum \vec{F}}{m_{sys}}$ is sometimes used. In these equations, $\vec{F}$ represents force, $m$ indicates mass, and $a$ is acceleration. 

This means that force is directly proportional to the mass and acceleration of an object. Using this formula, the acceleration of the system’s center of mass is in the same direction as the net force upon the system. 

Applications of Newton’s Second Law

This equation could now be applied to Kinematics and previous topics, utilizing the force to solve for acceleration or mass. 

For instance, if a cart was pushed across a surface with constant force and the mass is known, you could solve for the acceleration. From there, you could solve for the cart’s position, velocity, or time traveled, assuming other information was given. 

As force is a vector quantity, you could also break force down into components, using trigonometry to solve for the amount of force along the x or y axis. 

Alternatively, when multiple forces act upon a single object, individual forces can be combined with vector addition into a single net force. This net force is what  $\vec{F}=ma$ is applied to when solving for any of the 3 variables. 

There are also times when objects are moving together as a result of being pushed or are pulled with ropes attaching the objects. You can treat the entire system as one object by combining the masses. This total mass is used to find the system’s acceleration. Once the acceleration is known, you can apply it to each individual object to analyze specific forces acting on them, if necessary.

Practice