A = F_{net} / m

Definition

The equation $a = F_{net} / m$ represents the relationship between the net force ($F_{net}$) acting on an object, the object's mass ($m$), and the object's acceleration ($a$). This fundamental equation describes how the net force on an object determines its acceleration, which is a key concept in the study of classical mechanics.

5 Must Know Facts For Your Next Test

1. The equation $a = F_{net} / m$ is a fundamental relationship in classical mechanics that describes how the net force acting on an object determines its acceleration.
2. The net force, $F_{net}$, is the vector sum of all the forces acting on an object, including contact forces (e.g., normal, friction, tension) and non-contact forces (e.g., gravity, electric, magnetic).
3. The acceleration, $a$, is the rate of change of an object's velocity, and is a vector quantity with both magnitude and direction.
4. The mass, $m$, is a scalar quantity that represents the amount of matter in an object and is a measure of its inertia, or resistance to changes in motion.
5. The equation $a = F_{net} / m$ is used to predict the motion of objects under the influence of known net forces, and to analyze the forces acting on objects in various physical situations.

Review Questions

• Explain how the equation $a = F_{net} / m$ relates the net force acting on an object to its acceleration.
  • The equation $a = F_{net} / m$ states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to the object's mass. This means that if the net force on an object increases, its acceleration will also increase, and if the object's mass increases, its acceleration will decrease for the same net force. This relationship is a fundamental principle of classical mechanics and allows us to predict and analyze the motion of objects under the influence of known forces.
• Describe how the concept of inertia is related to the equation $a = F_{net} / m$.
  • The concept of inertia, which is an object's resistance to changes in its motion, is directly related to the equation $a = F_{net} / m$. An object's mass is a measure of its inertia, and the greater an object's mass, the more net force is required to change its motion, as described by the equation. This means that objects with greater mass will experience smaller accelerations than objects with less mass when subjected to the same net force, due to their greater inertia. The equation $a = F_{net} / m$ quantifies this relationship between an object's mass, the net force acting on it, and its resulting acceleration.
• Explain how the equation $a = F_{net} / m$ can be used to analyze changes in an object's momentum.
  • Momentum is the product of an object's mass and velocity, and is conserved in the absence of net external forces. The equation $a = F_{net} / m$ can be used to relate changes in an object's momentum to the net force acting on it. Specifically, the net force on an object is equal to the rate of change of the object's momentum, as described by the equation $F_{net} = dp/dt$, where $p$ is the object's momentum. By rearranging the equation $a = F_{net} / m$ to solve for $F_{net}$, we can see that the net force is also equal to the object's mass multiplied by its acceleration, $F_{net} = ma$. Combining these two equations, we can conclude that the rate of change of an object's momentum is equal to its mass multiplied by its acceleration, $dp/dt = ma$. This relationship allows us to analyze how the net force acting on an object affects changes in its momentum.

Related terms

Newton's Second Law: Newton's Second Law states that the net force acting on an object is equal to the object's mass multiplied by its acceleration, which is the mathematical expression $a = F_{net} / m$.

Inertia: Inertia is the property of an object that resists changes in its motion, and is directly related to the object's mass. The greater an object's mass, the greater its inertia and the more net force is required to change its motion, as described by $a = F_{net} / m$.

Momentum: Momentum is the product of an object's mass and velocity, and is conserved in the absence of net external forces. The equation $a = F_{net} / m$ is used to relate changes in an object's momentum to the net force acting on it.