Lt. John Drake
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- Overview
- What is Newton's second Law?
- What does net force mean?
- How do we use Newton's second law?
- What do we do when a force is directed at an angle?
- Example 1: Newton the turtle
- Example 2: String cheese
- GeneratedCaptionsTabForHeroSec
Review your understanding of Newton's second law in this free article aligned to NGSS standards.
What is Newton's second Law?
In the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
a=ΣFm
To be clear, a is the acceleration of the object, ΣF is the net force on the object, and m is the mass of the object.
In the world of introductory physics, Newton's second law is one of the most important laws you'll learn. It's used in almost every chapter of every physics textbook, so it's important to master this law as soon as possible.
We know objects can only accelerate if there are forces on the object. Newton's second law tells us exactly how much an object will accelerate for a given net force.
a=ΣFm
To be clear, a is the acceleration of the object, ΣF is the net force on the object, and m is the mass of the object.
[Wait, I thought Newton's second law was F=ma?]
Looking at the form of Newton's second law shown above, we see that the acceleration is proportional to the net force, ΣF , and is inversely proportional to the mass, m . In other words, if the net force were doubled, the acceleration of the object would be twice as large. Similarly, if the mass of the object were doubled, its acceleration would be half as large.
A force is a push or a pull, and the net force ΣF is the total force—or sum of the forces—exerted on an object. Adding vectors is a little different from adding regular numbers. When adding vectors, we must take their direction into account. The net force is the vector sum of all the forces exerted on an object.
[What does the term vector sum mean?]
For instance, consider the two forces of magnitude 30 N and 20 N that are exerted to the right and left respectively on the sheep shown above. If we assume rightward is the positive direction, the net force on the sheep can be found by
ΣF=30 N−20 N
ΣF=10 N to the right
If there were more horizontal forces, we could find the net force by adding up all the forces to the right and subtracting all the forces to the left.
If the problem you're analyzing has many forces in many directions, it's often easier to analyze each direction independently.
In other words, for the horizontal direction we can write
ax=ΣFxm
This shows that the acceleration ax in the horizontal direction is equal to the net force in the horizontal direction, ΣFx , divided by the mass.
Similarly, for the vertical direction we can write
ay=ΣFym
When forces are directed in diagonal directions, we can still analyze the forces in each direction independently. But, diagonal forces will contribute to the acceleration in both the vertical and horizontal directions.
For instance, let's say the force F3 on the hen is now directed at an angle θ as seen below.
The force F3 will affect both the horizontal and vertical accelerations, but only the horizontal component of F3 will affect horizontal acceleration; only the vertical component of F3 will affect the vertical acceleration. So we'll break the force F3 into horizontal and vertical components as seen below.
Now we see that the force F3 can be viewed as consisting of a horizontal force F3x and a vertical force F3y .
Using trigonometry, we can find the magnitude of the horizontal component with F3x=F3cosθ . Similarly, we can find the magnitude of the vertical component with F3y=F3sinθ .
[Wait, how did we find this?]
A 1.2 kg turtle named Newton has four forces exerted on it as shown in the diagram below.
What is the horizontal acceleration of Newton the turtle?
What is the vertical acceleration of Newton the turtle?
To find the horizontal acceleration we'll use Newton's second law for the horizontal direction.
ax=ΣFxm(Start with Newton’s 2nd law for the horizontal direction.)
ax=(30 N)cos30∘−22 N1.2 kg(Plug in horizontal forces with correct negative signs.)
A wedge of cheese is suspended at rest by two strings which exert forces of magnitude F1 and F2 , as seen below. There is also a downward force of gravity on the cheese of magnitude 20 N .
What is the magnitude of the force F1 ?
What is the magnitude of the force F2 ?
We'll start by either using the horizontal or vertical version of Newton's second law. We don't know the value of any of the horizontal forces, but we do know the magnitude of one of the vertical forces—20 N . Since we know more information about the vertical direction, we'll analyze that direction first.
ay=ΣFym(Start with Newton’s 2nd law for the vertical direction.)
ay=F1sin60∘−20 Nm(Plug in vertical forces with correct negative signs.)
Learn how to use Newton's second law to calculate the acceleration of an object for a given net force and mass. See how to add vectors, break forces into components, and apply the law to different scenarios.
Force is everywhere and it comes in a variety of sizes, directions, and type. We can define Force as the push or pull of an object. Learn Force definition, unit & types of Force with solved examples.
Sep 12, 2022 · The net (total) result is the force \(\vec{T}\). Similarly, when adhesive tape sticks to a piece of paper, the atoms of the tape are intermingled with those of the paper to cause a net electromagnetic force between the two objects.
Mar 20, 2023 · Air Force senior leaders from the active-duty, Reserve, Guard, and department civilians recently participated in a Department of the Air Force Total Force Integration, or TFI, symposium discussing how all components meet the demands of the total force.
Feb 1, 2011 · How the US military developed the Total Force concept to integrate active, reserve and Guard components after the Vietnam War. Learn about the political, military and historical factors that shaped the evolution of the Total Force.
The effect of all forces acting on a particular object can be represented by a single vector called the total force or the net force which is defined as the sum of all forces acting on that object: \[\vec F_{net}=\Sigma\vec F\]
